two-loop qcd correction to massive spin-2 …prepared for submission to jhep two-loop qcd correction...

Prepared for submission to JHEP

Two-Loop QCD Correction to massive spin-2

resonance → 3 gluons

Taushif Ahmed,a Maguni Mahakhud,a Prakash Mathews,b Narayan Ranaa and V.

Ravindranc

aHarish-Chandra Research Institute,

Chhatnag Road, Jhunsi, Allahabad 211 019, Uttar Pradesh, IndiabSaha Institute of Nuclear Physics,

1/AF Bidhan Nagar, Kolkata 700 064, IndiacThe Institute of Mathematical Sciences,

C.I.T Campus, 4th Cross St, Tharamani, Chennai 600 113, Tamil Nadu, India

E-mail: [email protected], [email protected],

[email protected], [email protected], [email protected]

Abstract: We present the O(α3s) virtual QCD corrections to the process h→ g+g+g due

to interference of born and two-loop amplitudes, where h is a massive spin-2 particle and g

is the gluon. We assume that the SM fields couple to h through the SM energy momentum

tensor. Our result constitutes one of the ingredients to full NNLO QCD contribution

to production of a massive spin-2 particle along with a jet in the scattering process at

the LHC. In particular, this massive spin-2 could be a KK mode of a ADD graviton in

large extra dimensional model or a RS KK mode in warped extra dimensional model or a

generic massive spin-2. In addition, it provides an opportunity to study the ultraviolet and

infrared structures of QCD amplitudes involving tensorial coupling resulting from energy

momentum operator. Using dimensional regularization, we find that infrared poles of

this amplitude are in agreement with the proposal by Catani confirming the factorization

property of QCD amplitudes with tensorial insertion.

Keywords: QCD, Spin-2 and NNLO calculation

arX

iv:1

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v1 [

hep-

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Contents

1 Introduction 1

2 Theory 3

2.1 The effective Lagrangian 3

2.2 Notation 4

2.3 Ultraviolet renormalization 4

2.4 Infrared factorization 5

3 Calculation of two-loop amplitude 6

3.1 Feynman diagrams and simplification 6

3.2 Reduction of tensor integrals 7

3.3 Master integrals 9

4 Results 10

5 Conclusion 11

A Harmonic polylogarithms 13

B One-loop coefficients 14

C Two-loop coefficients 15

1 Introduction

Theoretical studies on production and decay of a spin JP particle in the hadron colliders

in the Standard Model (SM) and its extensions are underway due to a wealth of informa-

tion available from ATLAS [1] and CMS [2] collaborations at the Large Hadron Collider

(LHC). In particular, investigations involving particles with higher spin, namely JP = 2+

bosons gained attention [3, 4] due to the discovery of a new boson at the LHC with a mass

m ≈ 125 GeV as its spin is yet to be determined with no doubt. Searches of spin-2 particles

earlier in Tevatron and recently in LHC were motivated due to their presence in theories

with large extra dimensions, such as ADD [5] and warped extra dimensions such as RS

[6] models. These beyond the SM (BSM) theories provide an alternate scenario to explain

the hierarchy problem of the SM through the introduction of compact higher dimensions

with factorisable (ADD) or non-factorisable (RS) geometries. The impact of these higher

dimensions can be understood in four dimensional framework through the existence of a

tower of massive spin-2 Kaluza-Klein (KK) gravitons. Their signatures at the colliders

can provide valuable information on these models. For the production of scalar JP = 0+

– 1 –

and vector JP = 1+ particles in the SM and BSM, there are extensive studies available

in literature. They include inclusive and semi-inclusive rates taking into account quantum

chromodynamics (QCD) and electroweak (EW) radiative corrections to impressively high

orders in perturbative expansion. Thanks to universal features of some of the perturbative

corrections in QCD, one can safely use those computed in the SM for BSM processes. For

spin-2 particles, searches in Drell-Yan (DY), di-photon and jet+missing energy at the LHC

are already underway. Also the bounds on the scale of the new physics and the number

of extra-dimensions are severely constrained from these searches. These studies use theo-

retical results computed in QCD at NLO level in perturbation theory. Such computations

are inevitable due to various uncertainties resulting from renormalization and factorization

scales as well as from the parton distribution functions. Needless to say that the correc-

tions are also big giving large K-factors which are often sensitive to the observables and

their physical scales. In ADD and RS models spin-2 KK gravitons contribute to physical

processes through either exchange of virtual graviton state or production of a real graviton

state. In the virtual mode, KK gravitons get exchanged between the SM particles and the

summation over their high multiplicity leads to a compensation of small coupling strength.

Hence, the cross section will be appreciable at collider energies, giving rise to non-resonant

enhancement of the high invariant mass regions of a di-final state production [7–9] or final

states involving more particles [10]. Next to leading order QCD corrections were computed

for the di-final state processes in the ADD model viz. `+`− [11–13], γγ [14, 15] and ZZ

[16, 17] and W+W− [18, 19], in addition they have been extended to NLO+PS accuracy

[20, 21]. On-shell spin-2 particle production results in missing energy signal. Again large

multiplicity of final states enhances the observable effects. Productions of on-shell spin-2

gravitons in association with (a) jet [22], (b) photon [23] and (c) electroweak gauge boson

[24] have been studied to NLO in QCD. Similar results taking into account NLO QCD

effects for processes involving the resonant production of spin-2 graviton are available for

di-lepton production [12, 13], di-photon production [15], di-neutral electroweak gauge bo-

son production [17] and charged electroweak gauge boson production W+W− [19]. Since

the NLO corrections and the associated scale uncertainties are not completely under con-

trol in most of the observable, an attempt [25] was undertaken to include soft and collinear

contribution to NNLO accuracy for processes involving KK gravitons in both ADD and

RS models. This was possible as the full two loop QCD matrix element of energy momen-

tum tensor is now available [26]. The phenomenological results show significant reduction

in dependence on renormalization and factorization scales and these results improve the

stability of the perturbative predictions.

Observables with jet + missing energy are sensitive to new physics from many BSM

scenarios. This missing energy could be due to a heavy resonance produced in the final state

escaping the detector. The NLO QCD effects to this process in large extra dimensional

model, namely ADD have been available for sometime and the importance of K-factor

and scale uncertainties are documented in [22]. In this article, we compute O(α3s) virtual

correction in massless QCD to the process h → g + g + g due to interference of born

and two-loop amplitudes, where h is a massive spin-2 particle. The full NNLO analysis

also requires square of one loop amplitudes, real emission processes and appropriate mass

– 2 –

counter terms which we reserve for future work. We have assumed a minimal coupling

between massive spin-2 field and the fields of the SM. Hence our results are applicable

to scattering processes involving a massive spin-2 particle and three gluons such as a

massive graviton production with a jet in ADD and RS models or production of a massive

spin-2 Higgs like boson along with a jet after appropriate analytical continuation [27] of

kinematical variables to the respective physical regions. Similar computations with massive

spin-0 and spin-1 boson productions at two loop level in QCD exist in the literature for

the processes Higgs→ g + g + g [28] and g + g → V + jet, V = Z, γ [29] respectively.

Spin-2 field being a rank-2 tensor, we encounter for the first time the two loop am-

plitudes with higher tensorial integrals resulting from rank-2 derivative couplings of spin-2

fields with the SM ones. In addition, we encounter more than 2000 two loop Feynman am-

plitudes contributing due to the universal coupling of spin-2 field with all the SM particles.

While these increase technical complexities at the intermediate stages of computation, the

results confirm the universal infra-red structure of QCD amplitudes. In other words, we

find that soft and collinear divergences not only factorise but also agree with the predic-

tions from Catani’s work [30] (see also [31]) on two loop QCD amplitudes for multi-leg

processes. We also observe that there are no additional UV divergences as the interaction

is through energy momentum tensor of the SM which is conserved. Hence, our present

work is also useful to study the field theoretical structure of QCD amplitudes with tensor

operator insertions, in particular with the energy momentum tensor of the SM.

In the next section, we describe the generic effective Lagrangian that describes coupling

of spin-2 fields with those of the SM. Section 3 is devoted to the computational details.

Section 4 and Appendix contain our final results. In section 5, we conclude with our

findings.

2 Theory

2.1 The effective Lagrangian

We consider the SM with an additional spin-2 field hµν . We assume that the spin-2 field

couples minimally with the SM ones through the SM energy momentum tensor TSMµν . Since

we are interested only in the QCD effects of the process under study, we restrict ourselves

to the QCD part of TSMµν and hence the action reads [5, 6] as

S = SSM + Sh −κ

2

∫d4x TQCDµν (x) hµν(x) , (2.1)

where κ is a dimensionful coupling and TQCDµν is the energy momentum tensor of QCD

given by

TQCDµν = −gµνLQCD − F aµρF aρν −1

ξgµν∂

ρ(Aaρ∂σAaσ) +

1

ξ(Aaν∂µ(∂σAaσ) +Aaµ∂ν(∂σAaσ))

+i

4

[ψγµ(

−→∂ ν − igsT aAaν)ψ − ψ(

←−∂ ν + igsT

aAaν)γµψ + ψγν(−→∂ µ − igsT aAaµ)ψ

−ψ(←−∂ µ + igsT

aAaµ)γνψ]

+ ∂µωa(∂νω

a − gsfabcAcνωb)

– 3 –

+∂νωa(∂µω

a − gsfabcAcµωb). (2.2)

gs is the strong coupling constant and ξ is the gauge fixing parameter. The T a are genera-

tors and fabc are the structure constants of SU(3). Note that spin-2 fields couple to ghost

fields (ωa) [32] as well in order to cancel unphysical degrees of freedom of gluon fields (Aaµ).

2.2 Notation

We consider the decay of a massive spin-2 field into three gluons

h(q)→ g(p1) + g(p2) + g(p3). (2.3)

The associated Mandelstam variables are defined as

s ≡ (p1 + p2)2, t ≡ (p2 + p3)

2, u ≡ (p1 + p3)2 (2.4)

which satisfy

s+ t+ u = M2h ≡ Q2 (2.5)

where Mh is the mass of the spin-2 field. We also define the following dimensionless

invariants which appear in harmonic polylogarithms (HPL) [33] and 2dHPL [34, 35] as

x ≡ s/Q2, y ≡ u/Q2, z ≡ t/Q2 (2.6)

satisfying

x+ y + z = 1. (2.7)

2.3 Ultraviolet renormalization

We describe here the ultraviolet (UV) renormalization of the matrix elements of the decay

of a spin-2 resonance with minimal coupling up to second order in QCD perturbation

theory. We regularize the theory in d = 4 + ε dimensions and the dimensionful strong

coupling constant in d dimensions is made dimensionless one (gs) by introducing the scale

µ0. We expand the unrenormalized amplitude in powers of as = g2s/16π2 as

|M〉 =

(asµε0Sε

) 12

|M(0)〉+

(asµε0Sε

) 32

|M(1)〉+

(asµε0Sε

) 52

|M(2)〉+O(a3s) , (2.8)

where Sε = exp[ ε2(γE − ln 4π)] with Euler constant γE = 0.5772 . . . , results from loop

integrals beyond leading order. |M(i)〉 is the unrenormalized color-space vector representing

the ith loop amplitude. In MS scheme, the renormalized coupling constant as ≡ as(µ2R) at

renormalization scale µR is related to unrenormalized coupling constant as by

asµε0Sε =

asµεR

Z(µ2R)

=asµεR

[1 + as

2β0ε

+ a2s

(4β20ε2

+β1ε

)+O(a3s)

], (2.9)

– 4 –

where

β0 =

(11

3CA −

4

3TFnf

), β1 =

(34

3C2A −

20

3CATFnf − 4CFTFnf

)(2.10)

with CA = N , CF = (N2 − 1)/2N , TF = 1/2 and nf is the number of active quark

flavors. Since, the spin-2 resonance couples to the SM particles through energy momentum

tensor (eqn.(2.1)) which is conserved, the coupling constant κ is protected from any UV

renormalization. Hence, there will be no additional UV renormalization required other than

the strong coupling constant renormalization. Using the eqn.(2.9), we now can express |M〉(eqn.(2.8)) in powers of renormalized as with UV finite matrix elements |M(i)〉

|M〉 = (as)12

(|M(0)〉+ as|M(1)〉+ a2s|M(2)〉+O(a3s)

)(2.11)

where

|M(0)〉 =

(1

µεR

) 12

|M(0)〉 ,

|M(1)〉 =

(1

µεR

) 32 [|M(1)〉+ µεR

r12|M(0)〉

],

|M(2)〉 =

(1

µεR

) 52[|M(2)〉+ µεR

3r12|M(1)〉+ µ2εR

(r22− r21

8

)|M(0)〉

](2.12)

with

r1 =2β0ε, r2 =

(4β20ε2

+β1ε

). (2.13)

2.4 Infrared factorization

Beyond leading order, the UV renormalized matrix elements |M(i)〉, i > 0 contain di-

vergences arising from the infrared sector of massless QCD. They result from soft gluons

and collinear massless partons present in the loops. They will cancel against similar di-

vergences coming from real emission contributions in the infrared safe observables order

by order in as, thanks to KLN theorem [36, 37]. The infrared divergence structure and

their factorization property in QCD amplitudes have been well studied for long time. In

[30], Catani predicted the infrared divergences of multi-parton QCD amplitudes precisely

in dimensional regularization up to two loops excluding two loop single pole in ε. In [31],

Sterman and Tejeda-Yeomans provided a systematic way of understanding the structure of

infrared divergences using factorization properties of the scattering amplitudes along with

infrared evolution equations. They demonstrated the connection of single pole in ε to a

soft anomalous dimension matrix, later computed in [38, 39]. The structure of single pole

term for the electromagnetic and Higgs form factors was first shown in [40, 41]. Using soft

collinear effective field theory, Becher and Neubert [42] derived the exact formula for the

infra-red divergences of scattering amplitudes with an arbitrary number of loops and legs

in massless QCD including single pole in dimensional regularization. Using Wilson lines

– 5 –

for hard partons and soft and eikonal jet functions in dimensional regularization, Gardi

and Magnea also arrived at a similar all order result [43].

According to Catani’s prediction, the renormalized amplitudes |M(i)〉 for the process

(eqn.(2.3)) can be expressed in terms of the universal subtraction operators I(i)g (ε) as fol-

lows1

|M(1)〉 = 2 I(1)g (ε) |M(0)〉+ |M(1)fin〉

|M(2)〉 = 2 I(1)g (ε) |M(1)〉+ 4 I(2)g (ε) |M(0)〉+ |M(2)fin〉 (2.14)

where,

I(1)g (ε) =1

2

e−ε2γE

Γ(1 + ε2)Vsingg (ε)

[(− s

µ2R

) ε2

+(− t

µ2R

) ε2

+(− u

µ2R

) ε2

]

I(2)g (ε) = − 1

2I(1)g (ε)

[I(1)g (ε)− 2β0

ε

]+

eε2γE Γ(1 + ε)

Γ(1 + ε2)

[− β0

ε+K

]I(1)g (2ε)

+ H(2)g (ε) (2.15)

and

Vsingg (ε) = CA4

ε2− β0

ε, K =

(67

18− π2

6

)CA −

10

9TFnf (2.16)

H(2)g (ε) =

3

2ε

{C2A

(− 5

12− 11

24ζ2 −

1

2ζ3

)+ CAnf

(29

27+

1

12ζ2

)− 1

2CFnf −

5

27n2f

}(2.17)

3 Calculation of two-loop amplitude

We now describe the computation of 〈M(0)|M(1)〉 & 〈M(0)|M(2)〉 matrix elements where

all the Lorentz and color indices of external particles are summed over. The computation

involves large number of Feynman diagrams. We need to perform various algebraic sim-

plifications with Dirac, Lorentz and color indices before the loop integrals are evaluated.

Due to tensorial coupling of spin-2 resonance with the SM fields, the loops contain higher

rank tensor integrals as compared to the ones normally encountered in the SM processes.

We have systematically automated this computation using various symbolic manipulation

programs developed in house and few publicly available packages that use FORM [44] and

Mathematica. In the following, we describe the method in detail.

3.1 Feynman diagrams and simplification

We use QGRAF [45] to generate the Feynman diagrams. We find that there are 4 diagrams

at tree level, 108 at one loop and 2362 at two loops, leaving out tadpole and self energy

corrections to the external legs. The output of the QGRAF is then converted to the format

that is suitable for further symbolic manipulation using FORM and Mathematica. A set of

1The numerical coefficients 2 and 4 with I(i) come due to the different definition of as between ours and Catani.

– 6 –

FORM routines is used to perform simplification of the squared matrix elements involving

gluon and spin-2 resonance polarization and color sums. We have used Feynman gauge

throughout and for the external on-shell gluon legs, physical polarizations are summed

using ∑s

εµ(pi, s)εν∗(pi, s) = −gµν +

pµi qνi + qµi p

νi

p.q(3.1)

where, pi is the ith-gluon momentum and qi is the corresponding reference momentum

which is an arbitrary light-like 4-vector. We choose q1 = p2, q2 = p1 and q3 = p1 for

simplicity. The spin-2 polarization sum in d dimensions is given by [11]

Bµν;ρσ(q) =

(gµρ − qµqρ

q.q

)(gνσ − qνqσ

q.q

)+

(gµσ − qµqσ

q.q

)(gνρ − qνqρ

q.q

)− 2

d− 1

(gµν − qµqν

q.q

)(gρσ − qρqσ

q.q

)(3.2)

3.2 Reduction of tensor integrals

Beyond leading order, the resulting expressions involve tensorial one and two loop integrals

which need to be reduced to a set of scalar integrals using a convenient tensorial reduction

procedure. Tensorial reduction is quite straightforward at one loop level but not so at two

loop level and beyond. In addition, finding a minimal set of integrals after the tensorial

reduction is important to achieve the task with large number of Feynman integrals. A

systematic approach to deal with higher rank tensor integrals and large number of scalar

integrals is to use Integration by parts (IBP) [46] and Lorentz invariant (LI) [47] identities.

The IBP identities follow from the fact that in the dimensional regularization, the

integral of the total derivative with respect to any loop momenta vanishes, that is∫ddk1(2π)d

· · ·∫

ddkL(2π)d

∂

∂ki·(vj

1∏lD

nll

)= 0 (3.3)

where nl is an element of ~n = (n1, · · ·, nN ) with nl ∈ Z, L is the number of loops and Dlsare propagators which depend on the loop and external momenta and also masses. The

four vector vµj can be both loop and external momenta. Performing the differentiation on

the left hand side and expressing the scalar products of ki and pj linearly in terms of Dl’s,one obtains the IBP identities given by∑

i

aiJ(bi,1 + n1, ..., bi,N + nN ) = 0 (3.4)

where

J(~m) = J(m1, · · ·,mN ) =

∫ddk1(2π)d

· · · ddkL

(2π)d1∏lD

mll

(3.5)

with bi,j ∈ {−1, 0, 1} and ai are polynomial in nj . The LI identities follow from the fact that

the loop integrals are invariant under Lorentz transformations of the external momenta,

that is

pµi pνj

(∑k

pk[ν∂

∂pµ]k

)J(~n) = 0. (3.6)

– 7 –

While these identities are useful to express the tensorial integrals in terms of a set of

master integrals, in practice, the computation becomes tedious due to the appearance of

large variety of Feynman integrals involving different set of propagators each requiring a

set of IBP and LI identities independently. We have reduced such varieties to a few by

shifting the loop momenta suitably using an in-house algorithm which uses FORM. For

one-loop diagrams, we can express each Feynman integral to contain terms from one of the

following three sets:

{D, D1, D12, D123} , {D, D2, D23, D123} , {D, D3, D31, D123} (3.7)

where,

D = k21, Di = (k1 − pi)2, Dij = (k1 − pi − pj)2, Dijk = (k1 − pi − pj − pk)2 (3.8)

In each set in eqn.(3.7), D’s are linearly independent and form a complete basis in the

sense that any Lorentz invariant k1 · pi can be expressed in terms of D’s. At two loops,

there are nine independent Lorentz invariants involving loop momenta k1 and k2, namely

{(kα · kβ), (kα · pi)}, α, β = 1, 2; i = 1, ..., 3. After appropriate shifting of loop momenta,

we can express each two loop Feynman integral to contain terms belonging to one of the

following six sets:

{D0, D1, D2, D1;1, D2;1, D1;12, D2;12, D1;123, D2;123}

{D0, D1, D2, D1;2, D2;2, D1;23, D2;23, D1;123, D2;123}

{D0, D1, D2, D1;3, D2;3, D1;31, D2;31, D1;123, D2;123}

{D0, D1, D2, D1;1, D2;1, D0;3, D1;12, D2;12, D1;123}

{D0, D1, D2, D1;2, D2;2, D0;1, D1;23, D2;23, D1;123}

{D0, D1, D2, D1;3, D2;3, D0;2, D1;31, D2;31, D1;123} (3.9)

where,

D0 = (k1 − k2)2, Dα = k2α, Dα;i = (kα − pi)2, Dα;ij = (kα − pi − pj)2,

D0;i = (k1 − k2 − pi)2, Dα;ijk = (kα − pi − pj − pk)2 (3.10)

Given the fewer number of sets (eqns.(3.7) & (3.9)), it is easier to use IBP and LI

identities using Laporta algorithm [48]. These identities can be generated using publicly

available packages such as AIR [49], FIRE [50], REDUZE [51, 52], LiteRed [53, 54] etc. For

our computation, we use a Mathematica based package LiteRedV1.51 along with MintV1.1

[55]. This package has the option to exploit symmetry relations within each set and also

among different sets.

– 8 –

Figure 1. Planar topologies of master integrals

3.3 Master integrals

Using these IBP and LI identities, we reduce all the integrals that appear in our computa-

tion to a minimal set of master integrals. For one loop, we get two topologically different

master integrals namely box and bubble, see Fig.(1) and we find that the master integrals

with three propagators are absent. For two loops, we encounter 16 planar and 5 non-planar

topologies of master integrals. These master integrals can be related to those that were

– 9 –

Figure 2. Non-Planar topologies of master integrals

computed by Gehrmann and Remiddi in their seminal papers [34, 35]. In particular, our

set of master integrals does not contain integrals with irreducible numerator, instead we

have higher power of propagators. We use IBP and LI identities to express our set of mas-

ter integrals to those of [34, 35]. All the master integrals are drawn in Fig.(1) and Fig.(2)

up to different permutations of the external momenta p1, p2 and p3. We also observe that

some topologies like iXBox1 given in Fig.(2) are absent in our final result and find some

new topologies namely Glass3S and Kite1 given in Fig.(1) which are absent in the [34, 35]

and those are simply a product of two one loop topologies.

Substituting the master integrals computed by Gehrmann and Remiddi [34, 35] in

terms of HPLs and 2dHPLs, we obtain the unrenormalized matrix elements 〈M(0)|M(1)〉and 〈M(0)|M(2)〉. We use shuffle algebra to express product of lower weight HPLs as a

sum of higher weight HPLs. In the next section we present our results.

4 Results

The UV renormalized matrix elements 〈M(0)|M(1)〉 and 〈M(0)|M(2)〉 are computed using

the unrenormalized counter parts through

〈M(0)|M(1)〉 =

(1

µεR

)2 [〈M(0)|M(1)〉+ µεR

r12〈M(0)|M(0)〉

],

〈M(0)|M(2)〉 =

(1

µεR

)3 [〈M(0)|M(2)〉+ µεR

3r12〈M(0)|M(1)〉

+ µ2εR

(r22− r21

8

)〈M(0)|M(0)〉

]. (4.1)

Using eqn.(2.14), we can also express the renormalized matrix elements in terms of I(i)g (ε),

given by

〈M(0)|M(1)〉 = 2 I(1)g (ε) 〈M(0)|M(0)〉+ 〈M(0)|M(1)fin〉 ,

〈M(0)|M(2)〉 = 2 I(1)g (ε) 〈M(0)|M(1)〉+ 4 I(2)g (ε) 〈M(0)|M(0)〉+ 〈M(0)|M(2)fin〉 .(4.2)

– 10 –

Expanding the right hand side of equations (4.1 & 4.2) in powers of ε and comparing their

coefficients of O(ε0), we obtain 〈M(0)|M(1)fin〉 and 〈M(0)|M(2)fin〉.We find that all the poles in ε resulting from the soft and collinear partons in eqn.(4.1)

are in agreement with those of eqn.(4.2). This serves as an important check on our result.

In addition, it establishes the universal structure of infrared poles in QCD amplitudes

involving tensorial operator insertion. We also observe that the contributions resulting

from the gauge fixing term in eqn.(2.1) cancel exactly with those of ghosts confirming the

gauge independence of our result. As we anticipated, the eqn.(4.1) does not require any

over all operator renormalization constant due to the conservation of energy momentum

tensor and it can be made UV finite through strong coupling constant renormalization

(eqn.(2.9)) alone. Below we present our final results

〈M(0)|M(0)〉 = Fh A(0) ,

〈M(0)|M(1)fin〉 = Fh

{− β0

2A(0) ln

(−Q

2

µ2

)+(A(1)

1 ζ2 +A(1)2

)},

〈M(0)|M(2)fin〉 = Fh

{3β208A(0) ln2

(−Q

2

µ2

)

〈M(0)|M(2)finFh〉+(−3 C2

A ζ3 A(0) +A(2)1 ζ2 +A(2)

2

)ln

(−Q

2

µ2

)

〈M(0)|M(2)finFh〉+(A(2)

3 ζ22 +A(2)4 ζ3 +A(2)

5 ζ2 +A(2)6

)}(4.3)

where,

Fh = 16π2κ2N(N2 − 1

),

A(0) =4

stu

(s4 + 2s3(t+ u) + 3s2

(t2 + u2

)+ 2s

(t3 + u3

)+(t2 + tu+ u2

)2),

A(1)α = A(1)

α;CACA +A(1)

α;nfnf ,

A(2)α = A(2)

α;C2AC2A +A(2)

α;CAnf CAnf +A(2)α;CFnf CFnf +A(2)

α;n2fn2f . (4.4)

The coefficients A(i)α;C are given in the appendix except A(2)

6;CAnf, A(2)

6;CFnf& A(2)

6;n2f

which

can be found in the files A6Canf, A6Cfnf and A6nf2 respectively attached with this arXiv

submission.

5 Conclusion

The computation of one and two loop QCD results for the process h→ g+g+g is presented.

We use dimensional regularization to regulate both UV and IR divergences. Our result is

– 11 –

very general in the sense that it can be used for any scattering process involving production

of a massive spin-2 particle that has a universal coupling with the SM fields. We can use

it to study the production of a jet with missing energy due to KK graviton escaping the

detector or a process with resonant massive spin-2 particle in association with a jet. Since

the spin-2 field couples with the SM ones through rank-2 tensor, we not only encounter large

number of Feynman diagrams but also the formidable challenge of reducing one and two

loop Feynman integrals with high powers of loop momenta to scalar ones. The IBP and LI

identities reduce all such integrals to only few master integrals that were already computed

by Gehrmann and Remiddi. This computation is the first of the kind involving four point

function at two loop level in QCD with tensorial insertion and one massive external state.

We find that no overall UV renormalization is required due to the conservation of energy

momentum tensor. We also find that our results exhibit the right IR structure confirming

the factorization property of QCD amplitude even with tensorial insertion.

Acknowledgement

MM, TA and NR thank for the hospitality provided by the Institute of Mathematical

Sciences (IMSc) where the work was carried out. We thank the staff of IMSc computer

center for their help. We sincerely thank T. Gehrmann for providing us the master integrals

required for our computation. We thank R. N. Lee for his help with LiteRed, and A.V.

Smirnov and V.A. Smirnov for their suggestions with FIRE. Finally, we would like to thank

K. Hasegawa, M. K. Mandal and L. Tancredi for discussions and their valuable suggestions.

NR, TA and MM also like to thank their parents and siblings for their wonderful love and

continuous support.

– 12 –

A Harmonic polylogarithms

In this section, we briefly describe the definition and properties of HPL and 2dHPL. HPL is

represented by H(~mw; y) with a w-dimensional vector ~mw of parameters and its argument

y. w is called the weight of the HPL. The elements of ~mw belong to {1, 0,−1} through

which the following rational functions are represented

f(1; y) ≡ 1

1− y, f(0; y) ≡ 1

y, f(−1; y) ≡ 1

1 + y. (A.1)

The weight 1 (w = 1) HPLs are defined by

H(1, y) ≡ − ln(1− y), H(0, y) ≡ ln y, H(−1, y) ≡ ln(1 + y) . (A.2)

For w > 1, H(m, ~mw; y) is defined by

H(m, ~mw; y) ≡∫ y

0dx f(m,x) H(~mw;x), m ∈ 0,±1 . (A.3)

The 2dHPLs are defined in the same way as eqn.(A.3) with the new elements {2, 3} in ~mw

representing a new class of rational functions

f(2; y) ≡ f(1− z; y) ≡ 1

1− y − z, f(3; y) ≡ f(z; y) ≡ 1

y + z(A.4)

and correspondingly with the weight 1 (w = 1) 2dHPLs

H(2, y) ≡ − ln(

1− y

1− z

), H(3, y) ≡ ln

(y + z

z

). (A.5)

Properties

Shuffle algebra : A product of two HPL with weights w1 and w2 of the same argument y

is a combination of HPLs with weight (w1 + w2) and argument y, such that all possible

permutations of the elements of ~mw1 and ~mw2 are considered preserving the relative orders

of the elements of ~mw1 and ~mw2 ,

H(~mw1 ; y)H(~mw2 ; y) =∑

~mw = ~mw1] ~mw2

H(~mw; y). (A.6)

Integration-by-parts identities : The ordering of the elements of ~mw in an HPL with weight

w and argument y can be reversed using integration-by-parts and in the process, some

products of two HPLs are generated in the following way

H(~mw; y) ≡ H(m1,m2, ...,mw; y) = H(m1, y)H(m2, ...,mw; y)

− H(m2,m1, y)H(m3, ...,mw; y)

+ ...+ (−1)w+1H(mw, ...,m2,m1; y) . (A.7)

– 13 –

B One-loop coefficients

A(1)1;CA

= −4

stu

(s4

+ 2s3(t + u) + 3s

2(t2

+ u2)

+ 2s(t3

+ u3)

+ t4

+ u4)

A(1)1;nf

= −2

s

(t2

+ u2)

A(1)2;CA

=

{− 6(t + u)

4(11s

8+ 22(3t + u)s

7+(187t

2+ 64ut + 33 u

2)s6

+(330t

3+ 60ut

2+ 78u

2t + 22u

3)s5

+(396 t

4+ 14ut

3

+ 51u2t2

+ 36u3t+ 11u

4)s4

+ 2t(165t

4+ 7u t

3+ 6u

2t2

+ 7u3t+ 10u

4)s3

+ t2(187t

4+ 60ut

3+ 51u

2t2

+ 14u3t+ 24u

4)s2

+ 2t3(33t

4+ 32ut

3+ 39u

2t2

+ 18u3t+ 10u

4)s+ 11t

4(t2

+ut+u2)2)

H(0, y)(s+u)4− 36 (s+ t)

4(t+u)

4(s4

+ 2(t+u)s3

+ 3(t2

+ u2)s2

+ 2(t3

+ u3)s + t

4+ u

4)H(0, y)H(0, z)(s + u)

4+ 6(s + t)

4((

11t4

+ 20ut3

+ 24u2t2

+ 20u3t+ 11u

4)s4

+ 2(11 t

5+ 18ut

4+ 7u

2t3

+ 7u3t2

+ 18u4t+ 11u

5)s3

+ 3(t+u)2(11t

4+ 4ut

3 − 2u2t2

+ 4u3t+ 11u

4)s2

+ 2(t+u)3(11 t

4

−ut3−u3t+ 11u

4)s+ 11(t+u)

4(t2

+ut+u2)2)

H(1, z)(s+u)4

+ 36(s+ t)4(t+u)

4(s4

+ 2ts3

+ 3t2s2

+ 2t3s+

(t2

+ut

+ u2)2)

H(0, y)H(1, z)(s+ u)4

+ 6(s+ t)4((

11t4

+ 20ut3

+ 24u2t2

+ 20u3t+ 11u

4)s4

+ 2(11 t

5+ 18ut

4+ 7u

2t3

+ 7u3t2

+18u4t+11u

5)s3

+3(t+u)2(11t

4+4ut

3−2u2t2

+4u3t+11u

4)s2

+2(t+u)3(11 t

4−ut3−u3t+11u

4)s+11(t+u)

4(t2

+ ut + u2)2)

H(2, y)(s + u)4

+ 36(s + t)4(t + u)

4(s4

+ 2us3

+ 3u2s2

+ 2u3s +

(t2

+ ut + u2)2)

H(0, z)H(2, y)(s + u)4

− 36(s + t)4(t + u)

4(2s

4+ 2(t + u)s

3+ 3

(t2

+ u2)s2

+ 2(t3

+ u3)s + 2

(t2

+ ut + u2)2)

H(1, z)H(3, y)(s + u)4

− 36(s + t)4

(t + u)4(s4

+ 2ts3

+ 3t2s2

+ 2t3s +

(t2

+ u t + u2)2)

H(0, 1, z)(s + u)4

+ 36(s + t)4(t + u)

4(s4

+ 2t s3

+ 3t2s2

+ 2t3s +

(t2

+ ut + u2)2)

H(0, 2, y)(s + u)4 − 36 (s + t)

4(t + u)

4(2s

4+ 2(2t + u)s

3+ 3

(2t

2+ u

2)s2

+ 2(2t

3

+ u3)s+ 2t

4+ 2u

4+ 2tu

3+ 3t

2u2

+ 2t3u)H(1, 0, y)(s+ u)

4 − 36(s+ t)4(t+ u)

4(s4

+ 2(t+ u)s3

+ 3(t2

+ u2)s2

+ 2(t3

+ u3)s + t

4+ u

4)H(1, 0, z) (s + u)

4+ 36(s + t)

4(t + u)

4(s4

+ 2ts3

+ 3t2s2

+ 2t3s +

(t2

+ u t + u2)2)

H(2, 0, y)(s + u)4

− 36(s + t)4(t + u)

4(2s

4+ 2 (t + u)s

3+ 3

(t2

+ u2)s2

+ 2(t3

+ u3)s + 2

(t2

+ u t + u2)2)

H(3, 2, y)(s + u)4

=− 2(s+ t)(t+ u)(203(t+ u)

3s10

+ 2(506t

4+ 1988ut

3+ 2973u

2t2

+ 1988u3t+ 506u

4)s9

+ 3(807t

5+ 3709ut

4+ 7123u

2t3

+ 7123u3t2

+ 3709u4t + 807 u

5)s8

+ 3(1208t

6+ 6186ut

5+ 13887u

2t4

+ 17836u3t3

+ 13887 u4t2

+ 6186u5t + 1208u

6)s7

+(3624t

7+ 21596ut

6+ 54318u

2t5

+ 80567u3t4

+ 80567u4t3

+ 54318u5t2

+ 21596u6t + 3624u

7)s6

+ 3(807t

8+ 6186ut

7

+ 18106u2t6

+ 29776u3t5

+ 34116u4t4

+ 29776u5t3

+ 18106u6t2

+ 6186u7t+ 807u

8)s5

+(1012 t

9+ 11127ut

8+ 41661u

2t7

+80567u3t6

+102348u4t5

+102348u5t4

+80567u6t3

+41661u7t2

+11127u8t+1012u

9)s4

+(203 t

10+3976ut

9+21369u

2t8

+53508u3t7

+80567u4t6

+89328u5t5

+80567u6t4

+53508u7t3

+21369u8t2

+3976u9t+203u

10)s3

+3tu(203t

9+1982ut

8

+ 7123u2t7

+ 13887u3t6

+ 18106u4t5

+ 18106u5t4

+ 13887u6t3

+ 7123u7t2

+ 1982u8t + 203u

9)s2

+ t2u2(t + u)

2(609t

6

+ 2758ut5

+ 5002u2t4

+ 5796u3t3

+ 5002 u4t2

+ 2758u5t + 609u

6)s + t

3u3(t + u)

3(203t

4+ 403u t

3+ 603u

2t2

+ 403u3t

+ 203u4))

(s+ u)− 6(s+ t)4(t+ u)

4(11s

8+ 22(t+ 3u)s

7+(33t

2+ 64ut+ 187u

2)s6

+(22 t

3+ 78ut

2+ 60u

2t+ 330u

3)s5

+(11t

4+36ut

3+51u

2t2

+14 u3t+396u

4)s4

+2u(10t

4+7ut

3+6u

2t2

+7u3t+165 u

4)s3

+u2(24t

4+14ut

3+51u

2t2

+60u3t

+187u4)s2

+2u3(10t

4+18ut

3+39u

2t2

+32u3t+33u

4)s+11u

4(t2

+ut+u2)2)

H(0, z)

}/(9st(s + t)

4u(s + u)

4(t + u)

4)

A(1)2;nf

=

{− 18u(s + u)

4(t + u)

4(s2 − ts + t

2+ u

2)H(1, 0, y)(s + t)

5+ 6 (t + u)

4(2s

8+ 4(t + 3u)s

7+ 2

(3t

2+ 5ut + 17u

2)s6

+(4t

3+ 15ut

2+ 6u

2t + 60u

3)s5

+ 2(t4

+ 12u2t2 − 2 u

3t + 36u

4)s4

+ 2u(t4 − 2ut

3+ 15u

2t2 − 2u

3t + 30 u

4)s3

+ 2u2(3t

4 − 2ut3

+ 12u2t2

+ 3u3t+ 17u

4)s2

+(12u

7+ 10tu

6+ 15t

2u5

+ 2t4u3)s+ 2u

4(t2

+ u t+ u2)2)

H(0, z)(s+ t)4

− 18tu(s + u)4(t + u)

4(t2

+ u2)H(0, y)H(0, z)(s + t)

4 − 6(s + u)4(2(t4

+ u t3

+ 3u2t2

+ u3t + u

4)s4

+ 4(t5 − u2

t3

− u3t2

+ u5)s3

+ 3(t+ u)2(2t

4+ ut

3+ 4u

2t2

+ u3t+ 2u

4)s2

+ 2(t+ u)3(2t

4 − ut3 − u3t+ 2u

4)s+ 2(t+ u)

4(t2

+ u t

+ u2)2)

H(1, z)(s + t)4

+ 18su(s + u)4(t + u)

4(s2

+ u2)H(0, y)H(1, z)(s + t)

4 − 6(s + u)4(2(t4

+ u t3

+ 3u2t2

+ u3t

+u4)s4

+ 4(t5 −u2

t3 −u3

t2

+u5)s3

+ 3(t+u)2(2t

4+ut

3+ 4u

2t2

+u3t+ 2u

4)s2

+ 2(t+u)3(2t

4 −ut3 −u3t+ 2u

4)s

+ 2(t+u)4(t2

+u t+u2)2)

H(2, y)(s+ t)4

+ 18st(s2

+ t2)(s+u)

4(t+u)

4H(0, z)H(2, y)(s+ t)

4− 18s(s+u)4(t+u)

5(s2

+ t2

+ u2 − t u

)H(1, z)H(3, y)(s + t)

4 − 18su(s + u)4(t + u)

4(s2

+ u2)H(0, 1, z)(s + t)

4+ 18su(s + u)

4(t + u)

4(s2

+u2)H(0, 2, y) (s+ t)

4− 18tu(s+u)4(t+u)

4(t2

+u2)H(1, 0, z)(s+ t)

4+ 18su (s+u)

4(t+u)

4(s2

+u2)H(2, 0, y)(s+ t)

4

– 14 –

=− 18s(s+ u)4(t+ u)

5(s2

+ t2

+ u2 − tu

)H(3, 2, y)(s+ t)

4+ 2(s+ u)(t+ u)

(35(t+ u)

3s10

+ 2(86t

4+ 335ut

3+ 507u

2t2

+ 335u3t + 86u

4)s9

+ 3(135t

5+ 607ut

4+ 1177u

2t3

+ 1177u3t2

+ 607u4t + 135u

5)s8

+ 3(200t

6+ 990ut

5+ 2211u

2t4

+ 2860u3t3

+ 2211u4t2

+ 990u5t + 200u

6)s7

+(600t

7+ 3428ut

6+ 8436u

2t5

+ 12593u3t4

+ 12593u4t3

+ 8436u5t2

+ 3428u6t+ 600u

7)s6

+ 3(135 t

8+ 990ut

7+ 2812u

2t6

+ 4612u3t5

+ 5328u4t4

+ 4612u5t3

+ 2812u6t2

+ 990u7t+ 135u

8)s5

= +(172t

9+ 1821ut

8+ 6633u

2t7

+ 12593 u3t6

+ 15984u4t5

+ 15984u5t4

+ 12593u6t3

+ 6633u7t2

+ 1821u8t + 172u

9)s4

+(35t

10+ 670ut

9+ 3531u

2t8

+ 8580u3t7

+ 12593u4t6

+ 13836u5t5

+ 12593u6t4

+ 8580u7t3

+ 3531u8t2

+ 670 u9t

+35u10)s3

+3tu(35t

9+338ut

8+1177u

2t7

+2211 u3t6

+2812u4t5

+2812u5t4

+2211u6t3

+1177u7t2

+338u8t+35 u

9)s2

+ t2u2(t+ u)

2(105t

6+ 460ut

5+ 796u

2t4

+ 918u3t3

+ 796u4t2

+ 460u5t+ 105u

6)s+ t

3u3(t+ u)

3(35t

4+ 67u t

3+ 99u

2t2

+ 67u3t + 35u

4))

(s + t) + 6(s + u)4(t + u)

4(2 s

8+ 4(3t + u)s

7+ 2

(17t

2+ 5ut + 3u

2)s6

+(60t

3+ 6u t

2+ 15u

2t

+ 4u3)s5

+ 2(36t

4 − 2ut3

+ 12u2t2

+ u4)s4

+ 2t(30t

4 − 2ut3

+ 15u2t2 − 2u

3t + u

4)s3

+ 2t2(17t

4+ 3ut

3+ 12u

2t2

− 2u3t + 3u

4)s2

+(12t

7+ 10u t

6+ 15u

2t5

+ 2u4t3)s + 2t

4(t2

+ ut + u2)2)

H(0, y)

}/(9st(s + t)

4u(s + u)

4(t + u)

4)

C Two-loop coefficients

A(2)

1;C2A

=11

stu

(s4

+ 2s3(t + u) + 3s

2(t2

+ u2)

+ 2s(t3

+ u3)

+ t4 − 2t

3u− 3t

2u2 − 2tu

3+ u

4)

A(2)1;CAnf

= −1

stu

(2s

4+ 4s

3(t + u) + 6s

2(t2

+ u2)

+ 4s(t3

+ u3)

+ 2t4 − 15t

3u− 6t

2u2 − 15tu

3+ 2u

4)

A(2)1;CF nf

= 0

A(2)

1;n2f

= −2

s

(t2

+ u2)

A(2)

2;C2A

=

{33(t+u)

4(11s

8+ 22(3t+u)s

7+(187t

2+ 64ut+ 33 u

2)s6

+(330t

3+ 60ut

2+ 78u

2t+ 22u

3)s5

+(396 t

4+ 14ut

3+ 51u

2t2

=+36u3t+11u

4)s4

+2t(165t

4+7u t

3+6u

2t2

+7u3t+10u

4)s3

+ t2(187t

4+60ut

3+51u

2t2

+14u3t+24u

4)s2

+2t3(33t

4+32ut

3

+ 39u2t2

+ 18u3t+ 10u

4)s+ 11t

4(t2

+ ut+ u2)2)

H(0, y) (s+ u)4

+ 198(s+ t)4(t+ u)

4(s4

+ 2(t+ u)s3

+ 3(t2

+ u2)s2

+ 2(t3

+u3)s+ t

4+u

4)H(0, y)H(0, z)(s+u)

4−33(s+ t)4((

11t4

+ 20ut3

+ 24u2t2

+ 20u3t+ 11u

4)s4

+ 2(11 t

5+ 18ut

4+ 7u

2t3

+ 7u3t2

+ 18u4t+ 11u

5)s3

+ 3(t+u)2(11t

4+ 4ut

3 − 2u2t2

+ 4u3t+ 11u

4)s2

+ 2(t+u)3(11 t

4 −ut3 −u3t+ 11u

4)s+ 11(t+u)

4(t2

+ut

+u2)2)

H(1, z)(s+u)4−198(s+ t)

4(t+u)

4(s4

+2ts3

+3t2s2

+2t3s+

(t2

+ut+u2)2)

H(0, y)H(1, z)(s+u)4−33(s+ t)

4((

11t4

+ 20ut3

+ 24u2t2

+ 20u3t+ 11u

4)s4

+ 2(11 t

5+ 18ut

4+ 7u

2t3

+ 7u3t2

+ 18u4t+ 11u

5)s3

+ 3(t+u)2(11t

4+ 4ut

3− 2u2t2

+ 4u3t

+ 11u4)s2

+ 2(t+ u)3(11 t

4 − ut3 − u3t+ 11u

4)s+ 11(t+ u)

4(t2

+ ut+ u2)2)

H(2, y)(s+ u)4 − 198(s+ t)

4(t+ u)

4(s4

+ 2us3

+ 3u2s2

+ 2u3s+

(t2

+ ut+ u2)2)

H(0, z)H(2, y)(s+ u)4

+ 198(s+ t)4

(t+ u)4(2s

4+ 2(t+ u)s

3+ 3(t2

+ u2)s2

+ 2(t3

+ u3)s

+ 2(t2

+ ut+ u2)2)

H(1, z)H(3, y) (s+ u)4

+ 198(s+ t)4(t+ u)

4(s4

+ 2ts3

+ 3t2s2

+ 2t3s+

(t2

+ u t+ u2)2)

H(0, 1, z)(s+ u)4

=− 198(s + t)4(t + u)

4(s4

+ 2t s3

+ 3t2s2

+ 2t3s +

(t2

+ ut + u2)2)

H(0, 2, y)(s + u)4

+ 198 (s + t)4(t + u)

4(2s

4+ 2(2t + u)s

3

+ 3(2t

2+ u

2)s2

+ 2(2t

3+ u

3)s + 2t

4+ 2u

4+ 2tu

3+ 3t

2u2

+ 2t3u)H(1, 0, y)(s + u)

4+ 198(s + t)

4(t + u)

4(s4

+ 2(t + u)s3

+ 3(t2

+ u2)s2

+ 2(t3

+ u3)s + t

4+ u

4)H(1, 0, z) (s + u)

4 − 198(s + t)4(t + u)

4(s4

+ 2ts3

+ 3t2s2

+ 2t3s +

(t2

+ u t

+u2)2)

H(2, 0, y)(s+u)4

+198(s+ t)4(t+u)

4(2s

4+2 (t+u)s

3+3(t2

+u2)s2

+2(t3

+u3)s+2

(t2

+u t+u2)2)

H(3, 2, y)(s+u)4

– 15 –

= + (s+ t)(t+ u)(1939(t+ u)

3s10

+(9662t

4+ 37856ut

3+ 56586u

2t2

+ 37856u3t+ 9662u

4)s9

+ 3(7701t

5+ 35213ut

4+ 67475u

2t3

+ 67475u3t2

+ 35213u4t+ 7701u

5)s8

+ 3(11524t

6+ 58638ut

5+ 131001u

2t4

+ 167972 u3t3

+ 131001u4t2

+ 58638u5t+ 11524u

6)s7

+(34572 t

7+ 204628ut

6+ 511062u

2t5

+ 754525u3t4

+ 754525u4t3

+ 511062u5t2

+ 204628u6t + 34572u

7)s6

+ 3(7701t

8

+ 58638ut7

+ 170354 u2t6

+ 278144u3t5

+ 317652u4t4

+ 278144u5t3

+ 170354u6t2

+ 58638 u7t+ 7701u

8)s5

+(9662t

9+ 105639ut

8

+393003u2t7

+754525 u3t6

+952956u4t5

+952956u5t4

+754525u6t3

+393003u7t2

+105639 u8t+9662u

9)s4

+(1939t

10+37856ut

9

+ 202425u2t8

+ 503916u3t7

+ 754525u4t6

+ 834432u5t5

+ 754525u6t4

+ 503916u7t3

+ 202425u8t2

+ 37856u9t + 1939u

10)s3

+3tu(1939 t

9+18862ut

8+67475u

2t7

+131001u3t6

+170354u4t5

+170354u5t4

+131001u6t3

+67475u7t2

+18862u8t+1939u

9)s2

+ t2u2

(t+u)2(5817t

6+ 26222ut

5+ 47378u

2t4

+ 54936u3t3

+ 47378u4t2

+ 26222u5t+ 5817u

6)s+ t

3u3(t+u)

3(1939t

4+ 3845u t

3

+5751u2t2

+3845u3t+1939u

4))

(s+u)+33(s+t)4(t+u)

4(11s

8+22(t+3u)s

7+(33t

2+64ut+187u

2)s6

+(22 t

3+78ut

2+60u

2t

+330u3)s5

+(11t

4+36ut

3+51u

2t2

+14 u3t+396u

4)s4

+2u(10t

4+7ut

3+6u

2t2

+7u3t+165 u

4)s3

+u2(24t

4+14ut

3+51u

2t2

+60u3t+187u

4)s2

+2u3(10t

4+18ut

3+39u

2t2

+32u3t+33u

4)s+11u

4(t2

+ut+u2)2)

H(0, z)

}/(9st(s + t)

4u(s + u)

4(t + u)

4)

A(2)2;CAnf

= −{

3(t+u)4(44s

8+ 88(3t+u)s

7+ 2(374t

2+ 119ut+ 66 u

2)s6

+(1320t

3+ 186ut

2+ 321u

2t+ 88u

3)s5

+ 2(792t

4− 8ut3

= + 183u2t2

+ 36u3t+ 22u

4)s4

+ 2t(660 t

4 − 8ut3

+ 177u2t2 − 8u

3t+ 31u

4)s3

+ 2t2(374t

4+ 93u t

3+ 183u

2t2 − 8u

3t+ 57u

4)s2

+ t3(264t

4+ 238ut

3+ 321 u

2t2

+ 72u3t + 62u

4)s + 44t

4(t2

+ ut + u2)2)

H(0, y)(s + u)4

+ 9(s + t)4(t + u)

4(4s

4+ 8(t + u)s

3

+ 12(t2

+ u2)s2

+ 8(t3

+ u3)s + 4t

4+ 4u

4 − 11tu3 − 11 t

3u)H(0, y)H(0, z)(s + u)

4 − 3(s + t)4(2(22t

4+ 31u t

3+ 57u

2t2

+ 31u3t + 22u

4)s4

+ 8(11t

5+ 9ut

4 − 2u2t3 − 2 u

3t2

+ 9u4t + 11u

5)s3

+ 3(t + u)2(44t

4+ 19ut

3+ 40u

2t2

+ 19u3t + 44u

4)s2

+ 2(t+ u)3(44t

4 − 13ut3 − 13u

3t+ 44 u

4)s+ 44(t+ u)

4(t2

+ ut+ u2)2)

H(1, z)(s+ u)4 − 9 (s+ t)

4(t+ u)

4(4s

4+ (8t− 11u)s

3

+ 12t2s2

+(8t

3 − 11 u3)s + 4

(t2

+ ut + u2)2)

H(0, y)H(1, z)(s + u)4 − 3 (s + t)

4(2(22t

4+ 31ut

3+ 57u

2t2

+ 31u3t + 22u

4)s4

+ 8(11t

5+ 9ut

4 − 2u2t3 − 2u

3t2

+ 9u4t + 11u

5)s3

+ 3 (t + u)2(44t

4+ 19ut

3+ 40u

2t2

+ 19u3t + 44u

4)s2

+ 2 (t + u)3(44t

4

− 13ut3 − 13u

3t+ 44u

4)s+ 44(t+ u)

4(t2

+ ut+ u2)2)

H(2, y)(s+ u)4 − 9(s+ t)

4(t+ u)

4(4 s

4+ (8u− 11t)s

3+ 12u

2s2

+(8u

3

− 11t3)s + 4

(t2

+ u t + u2)2)

H(0, z)H(2, y)(s + u)4

+ 9(s + t)4(t + u)

4(8s

4 − 3 (t + u)s3

+ 12(t2

+ u2)s2 − 3

(t3

+ u3)s

+ 8(t2

+ u t + u2)2)

H(1, z)H(3, y)(s + u)4

+ 9(s + t)4(t + u)

4(4s

4+ (8 t− 11u)s

3+ 12t

2s2

+(8t

3 − 11u3)s + 4

(t2

+ u t

+ u2)2)

H(0, 1, z)(s+ u)4 − 9(s+ t)

4(t+ u)

4(4s

4+ (8t− 11 u)s

3+ 12t

2s2

+(8t

3 − 11u3)s+ 4

(t2

+ u t+ u2)2)

H(0, 2, y)(s+ u)4

+ 9(s+ t)4(t+ u)

4(8s

4+ (16t− 3 u)s

3+ 12

(2t

2+ u

2)s2

+(16t

3 − 3u3)s+ 8t

4+ 8 u

4 − 3tu3

+ 12t2u2 − 3t

3u)H(1, 0, y)(s+ u)

4

+ 9(s + t)4(t + u)

4(4s

4+ 8(t + u)s

3+ 12

(t2

+ u2)s2

+ 8(t3

+ u3)s + 4t

4+ 4u

4 − 11tu3 − 11t

3u)H(1, 0, z)(s + u)

4

− 9(s+ t)4(t+ u)

4(4s

4+ (8t− 11u)s

3+ 12t

2s2

+(8t

3 − 11u3)s+ 4

(t2

+ ut+ u2)2)

H(2, 0, y)(s+ u)4

+ 9(s+ t)4(t+ u)

4(8 s

4

−3(t+u)s3

+12(t2

+u2)s2−3

(t3

+u3)s+8

(t2

+ut+u2)2)

H(3, 2, y)(s+u)4

+(s+t)(t+u)(499 (t+u)

3s10

+2(1228t

4+4741ut

3

= + 7143u2t2

+ 4741u3t + 1228 u

4)s9

+ 3(1931t

5+ 8547ut

4+ 16389u

2t3

+ 16389u3t2

+ 8547 u4t + 1931u

5)s8

+ 3(2864t

6

+ 13918ut5

+ 30487u2t4

+ 39100 u3t3

+ 30487u4t2

+ 13918u5t + 2864u

6)s7

+(8592t

7+ 48196u t

6+ 115584u

2t5

+ 168841u3t4

+ 168841u4t3

+ 115584u5t2

+ 48196u6t + 8592u

7)s6

+ 3(1931t

8+ 13918ut

7+ 38528u

2t6

+ 61228u3t5

+ 69608u4t4

+ 61228u5t3

+ 38528u6t2

+ 13918u7t + 1931u

8)s5

+(2456t

9+ 25641ut

8+ 91461u

2t7

+ 168841u3t6

+ 208824u4t5

+ 208824u5t4

+ 168841u6t3

+ 91461u7t2

+ 25641u8t+ 2456u

9)s4

+(499t

10+ 9482ut

9+ 49167u

2t8

+ 117300u3t7

+ 168841u4t6

+ 183684u5t5

+ 168841u6t4

+ 117300u7t3

+ 49167u8t2

+ 9482u9t+ 499u

10)s3

+ 3tu(499t

9+ 4762ut

8+ 16389u

2t7

+ 30487 u3t6

+ 38528u4t5

+ 38528u5t4

+ 30487u6t3

+ 16389u7t2

+ 4762u8t + 499u

9)s2

+ t2u2(t + u)

2(1497t

6+ 6488ut

5+ 11168u

2t4

+ 12930u3t3

+ 11168u4t2

+ 6488u5t + 1497u

6)s + t

3u3(t + u)

3(499t

4+ 959ut

3+ 1419u

2t2

+ 959u3t + 499u

4))

(s + u)

+ 3 (s + t)4(t + u)

4(44s

8+ 88(t + 3u)s

7+ 2

(66t

2+ 119ut + 374 u

2)s6

+(88t

3+ 321ut

2+ 186u

2t + 1320u

3)s5

+ 2(22t

4

+ 36ut3

+ 183u2t2 − 8u

3t + 792u

4)s4

+ 2u(31 t

4 − 8ut3

+ 177u2t2 − 8u

3t + 660u

4)s3

+ 2u2(57t

4 − 8u t3

+ 183u2t2

+ 93u3t

+ 374u4)s2

+ u3(62t

4+ 72ut

3+ 321 u

2t2

+ 238u3t+ 264u

4)s+ 44u

4(t2

+ ut+ u2)2)

H(0, z)

}/(9st(s + t)

4u(s + u)

4(t + u)

4)

A(2)2;CF nf

= −{

8(s4

+ 2s3(t + u) + 3s

2(t2

+ u2)

+ 2s(t3

+ u3)

+(t2

+ tu + u2)2)}/(

stu)

– 16 –

A(2)

2;n2f

=

{− 18u(s + u)

4(t + u)

4(s2 − ts + t

2+ u

2)H(1, 0, y)(s + t)

5+ 6 (t + u)

4(2s

8+ 4(t + 3u)s

7+ 2

(3t

2+ 5ut + 17u

2)s6

= +(4t

3+ 15ut

2+ 6u

2t+ 60u

3)s5

+ 2(t4

+ 12u2t2 − 2 u

3t+ 36u

4)s4

+ 2u(t4 − 2ut

3+ 15u

2t2 − 2u

3t+ 30 u

4)s3

+ 2u2(3t

4 − 2ut3

+ 12u2t2

+ 3u3t+ 17u

4)s2

+(12u

7+ 10tu

6+ 15t

2u5

+ 2t4u3)s+ 2u

4(t2

+u t+u2)2)

H(0, z)(s+ t)4 − 18tu(s+u)

4(t+u)

4(t2

+ u2)H(0, y)H(0, z)(s+ t)

4 − 6(s+ u)4(2(t4

+ u t3

+ 3u2t2

+ u3t+ u

4)s4

+ 4(t5 − u2

t3 − u3

t2

+ u5)s3

+ 3(t+ u)2(2t

4+ ut

3

+ 4u2t2

+u3t+ 2u

4)s2

+ 2(t+u)3(2t

4−ut3−u3t+ 2u

4)s+ 2(t+u)

4(t2

+u t+u2)2)

H(1, z)(s+ t)4

+ 18su(s+u)4(t+u)

4(s2

+ u2)H(0, y)H(1, z)(s + t)

4 − 6(s + u)4(2(t4

+ u t3

+ 3u2t2

+ u3t + u

4)s4

+ 4(t5 − u2

t3 − u3

t2

+ u5)s3

+ 3(t + u)2(2t

4

+ ut3

+ 4u2t2

+ u3t + 2u

4)s2

+ 2(t + u)3(2t

4 − ut3 − u3t + 2u

4)s + 2(t + u)

4(t2

+ u t + u2)2)

H(2, y)(s + t)4

+ 18st(s2

+ t2)(s + u)

4(t + u)

4H(0, z)H(2, y)(s + t)

4 − 18s(s + u)4(t + u)

5(s2

+ t2

+ u2 − t u

)H(1, z)H(3, y)(s + t)

4

− 18su(s + u)4(t + u)

4(s2

+ u2)H(0, 1, z)(s + t)

4+ 18su(s + u)

4(t + u)

4(s2

+ u2)H(0, 2, y) (s + t)

4 − 18tu(s + u)4(t + u)

4(t2

+u2)H(1, 0, z)(s+ t)

4+ 18su (s+u)

4(t+u)

4(s2

+u2)H(2, 0, y)(s+ t)

4−18s(s+u)4(t+u)

5(s2

+ t2

+u2− tu

)H(3, 2, y)(s+ t)

4

+6(s+u)(t+u)(5(t+u)

3s10

+6(4t

4+15ut

3+23u

2t2

+15u3t+4u

4)s9

+(55 t

5+227ut

4+437u

2t3

+437u3t2

+227u4t+55u

5)s8

=+(80 t

6+350ut

5+731u

2t4

+940u3t3

+731u4t2

+350u5t+80u

6)s7

+(80t

7+396ut

6+852u

2t5

+1211u3t4

+1211u4t3

+852u5t2

+396u6t+80u

7)s6

+(55t

8+350ut

7+852u

2t6

+1252u3t5

+1408u4t4

+1252u5t3

+852u6t2

+350u7t+55u

8)s5

+(24t

9+227ut

8

+ 731u2t7

+ 1211u3t6

+ 1408u4t5

+ 1408u5t4

+ 1211u6t3

+ 731u7t2

+ 227u8t + 24u

9)s4

+(5t

10+ 90u t

9+ 437u

2t8

+ 940u3t7

+ 1211u4t6

+ 1252u5t5

+ 1211u6t4

+ 940u7t3

+ 437u8t2

+ 90u9t+ 5u

10)s3

+ tu(15t

9+ 138ut

8+ 437 u

2t7

+ 731u3t6

+ 852u4t5

+ 852u5t4

+ 731u6t3

+ 437u7t2

+ 138u8t+ 15u

9)s2

+ t2u2(t+ u)

2(15t

6+ 60ut

5+ 92u

2t4

+ 106u3t3

+ 92u4t2

+ 60u5t+ 15u

6)s

+ t3u3(t+u)

3(5t

4+ 9u t

3+ 13u

2t2

+ 9u3t+ 5u

4))

(s+ t) + 6(s+u)4(t+u)

4(2 s

8+ 4(3t+u)s

7+ 2(17t

2+ 5ut+ 3u

2)s6

+(60t

3

+ 6u t2

+ 15u2t + 4u

3)s5

+ 2(36t

4 − 2ut3

+ 12u2t2

+ u4)s4

+ 2t(30t

4 − 2ut3

+ 15u2t2 − 2u

3t + u

4)s3

+ 2t2(17t

4+ 3ut

3

+ 12u2t2 − 2u

3t+ 3u

4)s2

+(12t

7+ 10u t

6+ 15u

2t5

+ 2u4t3)s+ 2t

4(t2

+ ut+ u2)2)

H(0, y)

}/(9st(s + t)

4u(s + u)

4(t + u)

4)

A(2)

3;C2A

={

49s4

+ 98s3

(t + u) + 147s2(t2

+ u2)

+ 98s(t3

+ u3)

+ 49t4 − 450t

3u + 165t

2u2 − 450tu

3+ 49u

4}/(

5stu)

A(2)3;CAnf

={

353t2 − 588tu + 353u

2}/(

5s)

A(2)3;CF nf

= −18{t2

+ u2}/(

s)

A(2)

3;n2f

= 0

A(2)

4;C2A

=

{9s

2t2u2(231s

16+ 1896(t + u)s

15+ 6

(1205t

2+ 2582u t + 1205u

2)s14

+ 2(8485t

3+ 28497ut

2+ 28497u

2t + 8485 u

3)s13

= +(27247t

4+ 132002ut

3+ 187458u

2t2

+ 132002u3t+ 27247u

4)s12

+ 12(2609t

5+ 18137ut

4+ 32471u

2t3

+ 32471 u3t2

+ 18137u4t

+2609u5)s11

+(26071t

6+265278u t

5+584223u

2t4

+758272u3t3

+584223u4t2

+265278u5t+26071 u

6)s10

+2(7765t

7+118994ut

6

+329001u2t5

+544812u3t4

+544812u4t3

+329001u5t2

+118994u6t+7765u

7)s9

+3(2110t

8+50618ut

7+186907u

2t6

+405032u3t5

+ 468376u4t4

+ 405032u5t3

+ 186907u6t2

+ 50618u7t+ 2110u

8)s8

+ 4(398t

9+ 16089ut

8+ 86178u

2t7

+ 272710u3t6

+ 333261u4t5

+ 333261 u5t4

+ 272710u6t3

+ 86178u7t2

+ 16089u8t+ 398u

9)s7

+(187t

10+ 16046ut

9+ 137715u

2t8

+ 724384u3t7

+ 1065452u4t6

+947616u5t5

+1065452u6t4

+724384u7t3

+137715u8t2

+16046u9t+187u

10)s6

+6tu(299t

9+5160ut

8+51597u

2t7

+106788 u3t6

+101934u4t5

+101934u5t4

+106788u6t3

+51597u7t2

+5160u8t+299u

9)s5

+t2u2(2973t

8+74726ut

7+236013u

2t6

+329784u3t5

+314484u4t4

+329784u5t3

+236013u6t2

+74726u7t+2973u

8)s4

+12t3u3(651t

7+3762ut

6+9502u

2t5

+11138 u3t4

+11138u4t3

+ 9502u5t2

+ 3762u6t + 651u

7)s3

+ 3t4u4(1027t

6+ 7446ut

5+ 12323u

2t4

+ 11392u3t3

+ 12323u4t2

+ 7446u5t + 1027u

6)s2

+ 6t5u5(315t

5+ 904ut

4+ 837u

2t3

+ 837u3t2

+ 904u4t+ 315u

5)s+ t

6u6(215t

4+ 250ut

3+ 357u

2t2

+ 250u3t+ 215u

4))

(t+ u)6

=− 108s2t2(s+ t)

6u2(s+ u)

6(s4

+ 2(t+ u)s3

+ 3(t2

+ u2)s2

+ 2(t3

+ u3)s+ t

4+ u

4 − 12tu3

+ 18t2u2 − 24t

3u)H(0, y)(t+ u)

6

− 108s2t2

(s+ t)6u2(s+ u)

6(s4

+ 2(t+ u)s3

+ 3(t2

+ u2)s2

+ 2(t3

+ u3)s+ t

4+ u

4 − 24tu3

+ 18t2u2 − 12t

3u)H(0, z) (t+ u)

6

+216s2t2(s+ t)

6u3(s+u)

6(2s

3−6us2

+10u2s+3t

(2t

2−3ut+4u2))H(1, y)(t+u)

6+108s

2t2(s+ t)

6u2

(s+u)6(s4

+2(t−u)s3

+ 3(t2

+ 5u2)s2

+ 2(t3 − 9 u

3)s+ t

4+ u

4+ 18tu

3 − 9t2u2

+ 30t3u)H(1, z)(t+ u)

6+ 108 s

2t2(s+ t)

6u2(s+ u)

6(s4 − 2(t+ u)s

3

+ 15(t2

+ u2)s2 − 18

(t3

+ u3)s + t

4+ u

4+ 6tu

3+ 9t

2u2

+ 6t3u)H(2, y)(t + u)

6

}/(27s

3t3u3(s + t)

6(s + u)

6(t + u)

6)

– 17 –

A(2)4;CAnf

=

{9s

2t2u2(54s

16+ 420(t + u)s

15+ 24

(64t

2+ 93ut + 64 u

2)s14

+(3520t

3+ 6099ut

2+ 6099u

2t + 3520u

3)s13

= + 2(2821t

4+ 4943ut

3+ 9330u

2t2

+ 4943u3t+ 2821u

4)s12

+ 6(1106t

5+ 1697ut

4+ 6163u

2t3

+ 6163u3t2

+ 1697u4t+ 1106 u

5)s11

+(5810t

6+7365ut

5+65076u

2t4

+38726u3t3

+65076u4t2

+7365u5t+5810u

6)s10

+(3736t

7+3503u t

6+105864u

2t5

+17977u3t4

+17977u4t3

+105864u5t2

+3503u6t+3736u

7)s9

+3(560t

8+208ut

7+38974u

2t6

+8059u3t5−15308u

4t4

+8059u5t3

+38974u6t2

+ 208u7t + 560u

8)s8

+(472t

9+ 60ut

8+ 81318u

2t7 − 8215u

3t6

+ 18453u4t5

+ 18453 u5t4 − 8215u

6t3

+ 81318u7t2

+ 60u8t

+ 472u9)s7

+(62 t

10+ 229ut

9+ 37632u

2t8 − 50045u

3t7

+ 25292u4t6

+ 177060u5t5

+ 25292u6t4 − 50045u

7t3

+ 37632u8t2

+ 229u9t + 62u

10)s6

+ 3tu(24t

9+ 3679ut

8 − 12820u2t7

+ 195u3t6

+ 50191u4t5

+ 50191u5t4

+ 195u6t3 − 12820u

7t2

+ 3679u8t

+ 24u9)s5

+ 2 t2u2(735t

8 − 6322ut7

+ 3033u2t6

+ 30537u3t5

+ 41982u4t4

+ 30537u5t3

+ 3033u6t2 − 6322u

7t + 735u

8)s4

+ t3u3(− 1700t

7+ 5703ut

6+ 17862u

2t5

+ 21167u3t4

+ 21167u4t3

+ 17862 u5t2

+ 5703u6t− 1700u

7)s3

+ 12t4u4(109t

6

+ 190u t5

+ 297u2t4

+ 423u3t3

+ 297u4t2

+ 190u5t + 109u

6)s2 − 6t

5u5(12t

5 − 24ut4 − 209u

2t3 − 209u

3t2 − 24u

4t + 12u

5)s

= + t6u6(20t

4+ 131ut

3+ 174u

2t2

+ 131u3t + 20u

4))

(t + u)6 − 162s

2t3(s + t)

6u3(s + u)

6(8t

2 − 21ut

+ 17u2)H(0, y)(t + u)

6 − 162s2t3(s + t)

6u3(s + u)

6(17t

2 − 21ut + 8 u2)H(0, z)(t + u)

6 − 54s2t2(s + t)

6u3(s + u)

6(41s

3

− 42u s2

+ 5u2s + t

(50t

2 − 63ut + 23u2))H(1, y)(t + u)

6+ 54s

2t2(s + t)

6u3(s + u)

6(41s

3 − 42us2

+ 5u2s + t

(− 25t

2+ 63u t− 52u

2))H(1, z)(t + u)

6+ 54s

2t2(s + t)

6u2(s + u)

6(41(t + u)s

3 − 42(t2

+ u2)s2

+ 5(t3

+ u3)s− 2t u

(t2

+ u2))H(2, y)(t + u)

6

}/(27s

3t3u3(s + t)

6(s + u)

6(t + u)

6)

A(2)4;CF nf

=

{432s

3t2(s+ t)

6u2(s+u)

6(− 3s

2+ t

2+u

2− tu)H(2, y) (t+u)

7− 18s2t2u2(48s

16+ 384(t+u)s

15+ 12

(120t

2+ 227 ut

= + 120u2)s14

+(3360t

3+ 9087ut

2+ 9087u

2t + 3360 u

3)s13

+ 3(1808t

4+ 6521ut

3+ 8604u

2t2

+ 6521u3t + 1808 u

4)s12

+(6336t

5+ 30735ut

4+ 47598u

2t3

+ 47598u3t2

+ 30735u4t + 6336u

5)s11

+(5424t

6+ 36543ut

5+ 67614u

2t4

+ 73464u3t3

+ 67614u4t2

+ 36543u5t + 5424u

6)s10

+(3360t

7+ 32505ut

6+ 77922u

2t5

+ 91295u3t4

+ 91295u4t3

+ 77922u5t2

+ 32505u6t

+ 3360u7)s9

+ 3(480t

8+ 6939u t

7+ 23404u

2t6

+ 34497u3t5

+ 31012u4t4

+ 34497u5t3

+ 23404u6t2

+ 6939u7t + 480u

8)s8

+ 3(128t

9+ 2999ut

8+ 15226u

2t7

+ 33508u3t6

+ 30137u4t5

+ 30137u5t4

+ 33508u6t3

+ 15226u7t2

+ 2999u8t + 128u

9)s7

+(48t

10+ 2337ut

9+ 19494u

2t8

+ 70630u3t7

+ 86678u4t6

+ 65250u5t5

+ 86678u6t4

+ 70630u7t3

+ 19494u8t2

+ 2337u9t

+ 48u10)s6

+ 3tu(92t

9+ 1601u t

8+ 10417u

2t7

+ 20343u3t6

+ 17708u4t5

+ 17708u5t4

+ 20343u6t3

+ 10417u7t2

+ 1601u8t

+ 92u9)s5

+ 3t2u2(172t

8+ 2556 ut

7+ 8524u

2t6

+ 11797u3t5

+ 10692u4t4

+ 11797u5t3

+ 8524u6t2

+ 2556u7t + 172u

8)s4

+ t3u3(788t

7+ 5538ut

6+ 14103u

2t5

+ 16252u3t4

+ 16252u4t3

+ 14103u5t2

+ 5538u6t + 788u

7)s3

+ 3t4u4(148t

6

+ 959ut5

+ 1726u2t4

+ 1748u3t3

+ 1726u4t2

+ 959u5t + 148u

6)s2

+ 3t5u5(72t

5+ 265ut

4+ 347u

2t3

+ 347u3t2

+ 265u4t

+ 72u5)s + 2t

6u6(16t

4+ 39ut

3+ 54 u

2t2

+ 39u3t + 16u

4))

(t + u)6

+ 108s2t3(s + t)

6u3

(s + u)6(t2

+ 13u2)H(0, y)(t + u)

6

+ 108s2t3(s + t)

6u3

(s + u)6(13t

2+ u

2)H(0, z)(t + u)

6+ 108s

2t2(s + t)

6u3

(s + u)6(12s

3 − 4u2s + 13t

3+ tu

2)H(1, y)(t + u)

6

− 108s2t2

(s + t)6u3(s + u)

6(12s

3 − 4u2s− t

(t2

+ 13u2))

H(1, z)(t + u)6

}/(27s

3t3u3(s + t)

6(s + u)

6(t + u)

6)

A(2)

4;n2f

= 0

A(2)

5;C2A

=

{9s

2t2(s + t)

2u2(55s

14+ (330t + 416u)s

13+(935 t

2+ 1844ut + 1500u

2)s12

+ 30(55t

3+ 135ut

2+ 167u

2t + 115 u

3)s11

= +(1980t

4+ 5670ut

3+ 8826u

2t2

+ 8462u3t + 5643 u

4)s10

+ 2(825t

5+ 2487ut

4+ 6495u

2t3

+ 3799u3t2

+ 5061 u4t + 3426u

5)s9

+(935t

6+2568ut

5+15141u

2t4

+4070u3t3−1902u

4t2

+9678u5t+6231u

6)s8

+2(165t

7+443u t

6+6261u

2t5−139u

3t4−8575u

4t3

− 4065u5t2

+ 3881u6t + 2085 u

7)s7

+(55t

8+ 334ut

7+ 7728u

2t6 − 6262u

3t5 − 17396u

4t4 − 22194u

5t3 − 7172u

6t2

+ 5130u7t

+ 1950u8)s6

+ 2u(45 t

8+ 1695ut

7 − 3483u2t6 − 4305u

3t5 − 4851u

4t4 − 8249u

5t3 − 1455u

6t2

+ 1362u7t+ 284u

8)s5

+ u2(717t

8

− 2782ut7 − 1182u

2t6

+ 5322u3t5 − 4938u

4t4 − 7502u

5t3

+ 711u6t2

+ 998u7t + 77 u

8)s4 − 2tu

3(158t

7 − 735ut6 − 2541u

2t5

−2255u3t4

+577 u4t3

+150u5t2−512u

6t−82u

7)s3

+t2u4(717t

6+1098u t

5+2632u

2t4

+2622u3t3

+1308u4t2

+852u5t+234u

6)s2

+2 t3u5(45t

5+157ut

4+619u

2t3

+516u3t2

+340u4t+102 u

5)s+t

4u6(55t

4+134ut

3+207u

2t2

+134u3t+105 u

4))H(0, y)(t+u)

6

– 18 –

= + 9s2t2u2(s+u)

2(55s

14+ (416 t+ 330u)s

13+(1500t

2+ 1844ut+ 935u

2)s12

+ 30(115 t

3+ 167ut

2+ 135u

2t+ 55u

3)s11

+(5643t

4

+ 8462ut3

+ 8826 u2t2

+ 5670u3t + 1980u

4)s10

+ 2(3426t

5+ 5061ut

4+ 3799 u

2t3

+ 6495u3t2

+ 2487u4t + 825u

5)s9

+(6231t

6

+ 9678u t5 − 1902u

2t4

+ 4070u3t3

+ 15141u4t2

+ 2568u5t + 935u

6)s8

+ 2(2085t

7+ 3881ut

6 − 4065u2t5 − 8575u

3t4 − 139u

4t3

+ 6261u5t2

+ 443u6t + 165u

7)s7

+(1950t

8+ 5130ut

7 − 7172u2t6 − 22194u

3t5 − 17396u

4t4 − 6262u

5t3

+ 7728u6t2

+ 334u7t

+ 55 u8)s6

+ 2t(284t

8+ 1362ut

7 − 1455u2t6 − 8249u

3t5 − 4851 u

4t4 − 4305u

5t3 − 3483u

6t2

+ 1695u7t + 45u

8)s5

+ t2(77 t

8

+998ut7

+711u2t6−7502u

3t5−4938u

4t4

+5322u5t3−1182u

6t2−2782u

7t+717u

8)s4

+2t3u(82t

7+512ut

6−150u2t5−577u

3t4

+ 2255u4t3

+ 2541u5t2

+ 735u6t− 158u

7)s3

+ t4u2(234t

6+ 852ut

5+ 1308u

2t4

+ 2622u3t3

+ 2632u4t2

+ 1098u5t + 717u

6)s2

+2t5u3(102t

5+340ut

4+516u

2t3

+619u3t2

+157u4t+45u

5)s+t

6u4(105t

4+134ut

3+207u

2t2

+134u3t+55u

4))H(0, z)(t+u)

6

+108s2t2(s+t)

6u2

(s+u)6(3s

4+6(t+u)s

3+9(t2

+u2)s2

+6(t3

+u3)s+3t

4+3u

4−4tu3−6t

2u2−4t

3u)H(0, y) H(0, z)(t+u)

6

−18s2t2(s+ t)

2u2(s+u)

6(3s

8+2(51t+u) s

7+(486t

2+200ut+30u

2)s6

+6(179t

3+130ut

2+96u

2t+7u

3)s5

+2(687t

4+677ut

3

+ 945u2t2

+ 265u3t+ 29 u

4)s4

+ 2t(537t

4+ 677ut

3+ 1344u

2t2

+ 658u3t+ 170 u

4)s3

+ 2t2(243t

4+ 390ut

3+ 945u

2t2

+ 658u3t

+ 270 u4)s2

+ 2t3(51t

4+ 100ut

3+ 288u

2t2

+ 265u3t + 170 u

4)s + t

4(3t

4+ 2ut

3+ 30u

2t2

+ 42u3t + 58 u

4))H(1, y)(t + u)

6

=− 216s2t2(s + t)

6u3(s + u)

6(2 s

3 − 3us2

+ 4u2s + t

(2t

2 − 3ut + 4u2))H(0, z)H(1, y) (t + u)

6 − 108s2t2(s + t)

6u2(s + u)

6(3s

4

+ (6t− 8u)s3

+(9 t

2+ 6u

2)s2

+(6t

3 − 4u3)s + 3t

4+ 3u

4+ 12tu

3+ 6t

2u2

+ 16t3u)H(0, y)H(1, z)(t + u)

6

−1296s2t2(s+t)

6u3(s+u)

6(s3−us2 +u

2s+t

(t2−ut+u2

))H(1, y)H(1, z) (t+u)

6−108s2t2(s+t)

6u2(s+u)

6(3s

4+(2u−8t)s

3

+ 3(2 t

2+ 5u

2)s2 − 2

(2t

3+ u

3)s+ 3t

4+ 3u

4+ 8tu

3+ 12t

2u2

+ 8t3u)H(0, z)H(2, y)(t+ u)

6 − 108s2t2(s+ t)

6u2(s+ u)

6(8s

4

+(4t−2u)s3

+9(2t

2+3u

2)s2−2u

3s+8t

4+8 u

4+18tu

3+27t

2u2

+18t3u)H(1, z)H(2, y)(t+u)

6−108s2t2

(s+t)6u2(s+u)

6(2s

4

+ 10(t + u)s3 − 3

(t2

+ u2)s2

+ 6(t3

+ u3)s + 2

(t2

+ ut + u2)2)

H(1, z)H(3, y) (t + u)6 − 108s

2t3(s + t)

6u3(s + u)

6(6t

2 − 9ut

+ 2u2)H(0, 0, y)(t + u)

6 − 108s2t3(s + t)

6u3(s + u)

6(2t

2 − 9ut + 6 u2)H(0, 0, z)(t + u)

6+ 432s

2t2(s + t)

6u2(s + u)

6(2s

4

+2(2 t+u)s3

+3(2t

2+u

2)s2

+2(2t

3+u

3)s+2t

4+2 u

4+2tu

3+3t

2u2

+2t3u)H(0, 1, y)(t+u)

6+108s

2t2(s+ t)

6u2(s+u)

6(3s

4

+(6t−2u)s3

+3(3t

2+5u

2)s2

+2(3t

3+u

3)s+3t

4+3u

4−14tu3

+9t2u2−14t

3u)H(0, 1, z)(t+u)

6−108s2t2(s+t)

6u2(s+u)

6(3s

4

+8(t−u)s3

+6(2t

2+u

2)s2

+(8t

3−4u3)s+3

(t4

+6u t3−u2

t2

+6u3t+u

4))H(0, 2, y)(t+u)

6+108s

2t2(s+ t)

6u2(s+u)

6(6s

4

=+2(6t−u)s3

+3(6t

2+5u

2)s2

+2(6t

3+u

3)s+6t

4+6u

4+6tu

3+9t

2u2

+6t3u)H(1, 0, y)(t+u)

6+108s

2t2(s+t)

6u2(s+u)

6(3s

4

+2(3t+5u) s3

+3(3t

2+u

2)s2

+2(3t

3+7u

3)s+3t

4+3u

4−2 tu3−3t

2u2−2t

3u)H(1, 0, z)(t+u)

6+216s

2t2(s+t)

6u2

(s+u)6(4s

4

+8(t+u)s3

+3(4t

2+u

2)s2

+(8t

3+6 u

3)s+4t

4+4u

4+6tu

3+3t

2u2

+8t3u)H(1, 1, y) (t+u)

6+108s

2t2(s+ t)

6u3(s+u)

6(18s

3

− 3us2

+ 18u2s− t

(18t

2+ 9ut + 14u

2))H(1, 1, z)(t + u)

6 − 1296s2t2

(s + t)6u3(s + u)

6(s3 − us2 + u

2s + t

(t2 − ut

+ u2))

H(1, 2, y)(t + u)6 − 108s

2t2(s + t)

6u2(s + u)

6(3s

4+ 2(t− 4u)s

3+ 3

(5t

2+ 2u

2)s2 − 2

(t3

+ 2u3)s + 3t

4+ 3u

4+ 8t u

3

+ 12t2u2

+ 8t3u)H(2, 0, y)(t + u)

6 − 108s2t2(s + t)

6u3

(s + u)6(6s

3 − 9us2

+ 2u2s + t

(2t

2+ 3ut + 2u

2))

H(2, 1, y)(t + u)6

− 108s2t2(s + t)

6u2(s + u)

6(8s

4 − 2(t + u)s3

+ 27(t2

+ u2)s2 − 2

(t3

+ u3)s + 8

(t2

+ u t + u2)2)

H(2, 2, y)(t + u)6

− 108s2t2(s + t)

6u2(s + u)

6(2s

4+ 10(t + u)s

3 − 3(t2

+ u2)s2

+ 6(t3

+ u3)s + 2

(t2

+ ut + u2)2)

H(3, 2, y)(t + u)6

= + 9t2(s+ t)u

2(s+u)

(366(t+u)

6s16

+ 12(213t

7+ 1475ut

6+ 4463u

2t5

+ 7365u3t4

+ 7365u4t3

+ 4463u5t2

+ 1475u6t+ 213u

7)s15

+2(t+u)2(4186t

6+23989ut

5+61240u

2t4

+77078u3t3

+61240u4t2

+23989 u5t+4186u

6)s14

+2(8526t

9+72111ut

8+283103u

2t7

+ 646677u3t6

+ 948359u4t5

+ 948359u5t4

+ 646677u6t3

+ 283103u7t2

+ 72111u8t+ 8526u

9)s13

+ (t+ u)2(23886t

8+ 172264u t

7

+ 582649u2t6

+ 1131132u3t5

+ 1344162u4t4

+ 1131132u5t3

+ 582649 u6t2

+ 172264u7t+ 23886u

8)s12

+(23866t

11+ 243086u t

10

+ 1157425u2t9

+ 3382695u3t8

+ 6575795u4t7

+ 8973837u5t6

+ 8973837u6t5

+ 6575795u7t4

+ 3382695u8t3

+ 1157425u9t2

+ 243086 u10t + 23866u

11)s11

+ (t + u)2(17016t

10+ 164440u t

9+ 724400u

2t8

+ 1917401u3t7

+ 3236864u4t6

+ 3710558u5t5

+ 3236864 u6t4

+ 1917401u7t3

+ 724400u8t2

+ 164440u9t+ 17016u

10)s10

+ 2(4176t

13+ 58901ut

12+ 382615u

2t11

+ 1458232u3t10

+ 3634444u4t9

+ 6299163u5t8

+ 8074581u6t7

+ 8074581u7t6

+ 6299163u8t5

+ 3634444u9t4

+ 1458232u10t3

+ 382615u11

t2

+ 58901u12t + 4176u

13)s9

+ (t + u)2(2552t

12+ 42616u t

11+ 321337u

2t10

+ 1192960u3t9

+ 2636700u4t8

+ 3851544u5t7

+ 4187542u6t6

+ 3851544u7t5

+ 2636700u8t4

+ 1192960u9t3

+ 321337 u10t2

+ 42616u11t + 2552u

12)s8

+(366t

15+ 11590u t

14

+ 150117u2t13

+ 868535u3t12

+ 2906129u4t11

+ 6451075u5t10

+ 10280514u6t9

+ 12609962u7t8

+ 12609962u8t7

+ 10280514u9t6

– 19 –

= + 6451075u10t5

+ 2906129u11t4

+ 868535u12t3

+ 150117u13

t2

+ 11590u14t + 366u

15)s7

+ tu(t + u)2(1254t

12+ 30458 ut

11

+192025u2t10

+634366u3t9

+1369170u4t8

+2072140u5t7

+2324670u6t6

+2072140u7t5

+1369170u8t4

+634366u9t3

+192025 u10t2

+30458u11t+1254u

12)s6

+2t2u2(1605 t

13+19222ut

12+110551u

2t11

+398318u3t10

+989437u4t9

+1764628u5t8

+2329703u6t7

+ 2329703u7t6

+ 1764628u8t5

+ 989437 u9t4

+ 398318u10t3

+ 110551u11t2

+ 19222u12t + 1605 u

13)s5

+ t3u3(t + u)

2(1678t

10

+19862ut9

+93582u2t8

+253073u3t7

+439352u4t6

+520162u5t5

+439352u6t4

+253073u7t3

+93582u8t2

+19862u9t+1678u

10)s4

+ t4u4(t + u)

3(1260t

8+ 9096ut

7+ 30583u

2t6

+ 61244u3t5

+ 75426u4t4

+ 61244 u5t3

+ 30583u6t2

+ 9096u7t + 1260u

8)s3

+ t5u5(t+u)

4(324t

6+ 2168ut

5+ 6197u

2t4

+ 8622u3t3

+ 6197u4t2

+ 2168u5t+ 324u

6)s2

+ 10t6u6(t+u)

7(14t

2+ 27ut+ 14u

2)s

+40t7u7(t+u)

6(t2

+ut+u2))

+9s2t2u2(3(11t

6+130ut

5+141u

2t4

+604u3t3

+141u4t2

+130u5t+11 u

6)s16

+8(45t

7+521ut

6

+ 1056u2t5

+ 2598u3t4

+ 2488 u4t3

+ 858u5t2

+ 411u6t + 23u

7)s15

+ 6(285t

8+ 3120u t

7+ 8470u

2t6

+ 17852u3t5

+ 25104u4t4

= + 15024u5t3

+ 5642u6t2

+ 1908 u7t + 83u

8)s14

+ 2(2375t

9+ 24561ut

8+ 80646u

2t7

+ 164370 u3t6

+ 268500u4t5

+ 242676u5t4

+112746u6t3

+43806u7t2

+11685u8t+539u

9)s13

+(8669t

10+85044ut

9+320811u

2t8

+677420 u3t7

+1161930u4t6

+1394268u5t5

+895510u6t4

+373044u7t3

+149697 u8t2

+34384u9t+2343u

10)s12

+12(915t

11+8573u t

10+35593u

2t9

+81037u3t8

+140831u4t7

+205671u5t6

+184091u6t5

+94279u7t4

+41772u8t3

+16990u9t2

+3718u10t+370 u

11)s11

+(9845t

12+88872ut

11+394182u

2t10

+982076u3t9

+1680477u4t8

+2723040u5t7

+3377880u6t6

+2469456u7t5

+1323771u8t4

+704312u9t3

+264210u10t2

+55188 u11t

+ 6179u12)s10

+ 2(3095t

13+ 27024ut

12+ 127632 u

2t11

+ 352506u3t10

+ 563960u4t9

+ 824355u5t8

+ 1409056u6t7

+ 1665520u7t6

+ 1351875u8t5

+ 966790u9t4

+ 514400u10t3

+ 159702 u11t2

+ 28798u12t + 2919u

13)s9

+ 3(870t

14+ 7314u t

13+ 37677u

2t12

=+112780u3t11

+143003u4t10

+53282u5t9

+249844u6t8

+845260u7t7

+1239890u8t6

+1252614u9t5

+905087 u10t4

+401760u11t3

+ 101733u12t2

+ 14670u13t + 1176 u

14)s8

+ 4(166t

15+ 1359ut

14+ 8343u

2t13

+ 18170u3t12 − 29355u

4t11 − 193428u

5t10

− 186082u6t9

+ 373479u7t8

+ 1074360u8t7

+ 1349559u9t6

+ 1156713u10t5

+ 673434u11t4

+ 244731u12t3

+ 51600u13t2

+ 5604u14t

+ 307u15)s7

+(77t

16+ 712ut

15+ 7926u

2t14 − 22420u

3t13 − 310304u

4t12 − 964008u

5t11 − 1004190u

6t10

+ 1290836u7t9

+ 5018184u8t8

+ 6920472u9t7

+ 6102774u10t6

+ 3900588u11t5

+ 1764592u12

t4

+ 528392u13t3

+ 92178u14t2

+ 6772u15t

+ 187u16)s6

+ 6 tu(5t

15+ 338ut

14 − 3532u2t13 − 33260u

3t12 − 97374u

4t11 − 95800u

5t10

+ 181294u6t9

+ 739773u7t8

+ 1163599u8t7

+ 1123652u9t6

+ 758126u10t5

+ 368632u11t4

+ 127306u12t3

+ 29970u13t2

+ 4032u14t+ 151u

15)s5

+ t2u2(327 t

14

− 6804ut13 − 59454u

2t12 − 167472u

3t11 − 99128u

4t10

+ 699492u5t9

+ 2552097u6t8

+ 4572060u7t7

+ 5195055u8t6

+ 4069272u9t5

+ 2242188u10t4

+ 847572u11t3

+ 212250u12t2

+ 33688u13t+ 2793u

14)s4

+ 4t3u3(− 233t

13− 1616u t12− 3051u

2t11

+ 10663u3t10

= + 80192u4t9

+ 249270u5t8

+ 483611 u6t7

+ 633999u7t6

+ 583800u8t5

+ 382847u9t4

+ 174178u10t3

+ 51444 u11t2

+ 8727u12t

+ 617u13)s3

+ 3t4u4(t + u)

2(109 t

10+ 662ut

9+ 4205u

2t8

+ 17972u3t7

+ 46152u4t6

+ 74668u5t5

+ 76440u6t4

+ 53188u7t3

+ 24579u8t2

+ 6934u9t + 931u

10)s2

+ 2t5u5(t + u)

3(15t

8+ 481ut

7+ 3156u

2t6

+ 8739u3t5

+ 13780 u4t4

+ 12711u5t3

+ 7500u6t2

+ 2637u7t + 453u

8)s + t

6u6

(t + u)6(77t

4+ 270ut

3+ 477u

2t2

+ 350u3t + 187u

4))

H(1, z) + 9s2t2u2(3(13t

6

+ 142ut5

+ 171u2t4

+ 644u3t3

+ 171u4t2

+ 142u5t + 13u

6)s16

+ 8(50t

7+ 578ut

6+ 1293 u

2t5

+ 3103u3t4

+ 3103u4t3

+ 1293u5t2

+ 578u6t+ 50u

7)s15

+ 12(157t

8+ 1789ut

7+ 5420u

2t6

+ 12039u3t5

+ 17342u4t4

+ 12039u5t3

+ 5420u6t2

+ 1789u7t

+ 157u8)s14

+(5374 t

9+ 59826ut

8+ 223092u

2t7

+ 513996u3t6

+ 871536u4t5

+ 871536u5t4

+ 513996u6t3

+ 223092u7t2

+ 59826u8t + 5374u

9)s13

+(10359t

10+ 114484ut

9+ 503079u

2t8

+ 1279432u3t7

+ 2390090u4t6

+ 3044424u5t5

+ 2390090u6t4

+ 1279432u7t3

+ 503079 u8t2

+ 114484u9t + 10359u

10)s12

+ 12(1186t

11+ 13429u t

10+ 67778u

2t9

+ 197005u3t8

+ 403359u4t7

+ 605123u5t6

+ 605123u6t5

+ 403359u7t4

+ 197005u8t3

+ 67778u9t2

+ 13429u10t + 1186 u

11)s11

+(14195t

12+ 171720ut

11

+ 991722u2t10

+ 3343932u3t9

+ 7591317u4t8

+ 12777132u5t7

+ 15424700u6t6

+ 12777132u7t5

+ 7591317u8t4

+ 3343932u9t3

+ 991722u10

t2

+ 171720u11t + 14195u

12)s10

+ 2(5067t

13+ 68848u t

12+ 464430u

2t11

+ 1834210u3t10

+ 4687302u4t9

+ 8645967u5t8

+ 11943168u6t7

+ 11943168u7t6

+ 8645967u8t5

+ 4687302u9t4

+ 1834210u10t3

+ 464430u11t2

+ 68848u12t

+ 5067u13)s9

+ 3(1638t

14+ 26822ut

13+ 219527u

2t12

+ 1022692u3t11

+ 2994269u4t10

+ 6115342u5t9

+ 9403374u6t8

– 20 –

= + 10916304u7t7

+ 9403374u8t6

+ 6115342u9t5

+ 2994269u10t4

+ 1022692u11

t3

+ 219527u12t2

+ 26822u13t + 1638u

14)s8

+ 4(361 t

15+ 8109ut

14+ 85470u

2t13

+ 471328u3t12

+ 1600674u4t11

+ 3733632u5t10

+ 6488383u6t9

+ 8627643u7t8

+ 8627643u8t7

+ 6488383u9t6

+ 3733632u10t5

+ 1600674u11t4

+ 471328u12

t3

+ 85470u13t2

+ 8109u14t + 361u

15)s7

+(193 t

16+ 8108ut

15

+ 123366u2t14

+ 816896u3t13

+ 3259172u4t12

+ 8952972u5t11

+ 18149594u6t10

+ 27988696u7t9

+ 32478774u8t8

+ 27988696u9t7

+ 18149594u10t6

+ 8952972u11t5

+ 3259172u12t4

+ 816896u13t3

+ 123366u14t2

+ 8108u15t+ 193u

16)s6

+ 6tu(157t

15+ 4612ut

14

+ 39024u2t13

+ 191670u3t12

+ 643658u4t11

+ 1557030u5t10

+ 2799334u6t9

+ 3770803u7t8

+ 3770803u8t7

+ 2799334u9t6

+ 1557030u10t5

+ 643658u11t4

+ 191670u12t3

+ 39024u13t2

+ 4612u14t+ 157u

15)s5

+ t2u2(2883t

14+ 38608ut

13+ 269730u

2t12

+ 1182108u3t11

+ 3470348u4t10

+ 7219608u5t9

+ 11105895u6t8

+ 12818744u7t7

+ 11105895u8t6

+ 7219608u9t5

+ 3470348u10t4

+ 1182108u11t3

+ 269730u12t2

+ 38608u13t+ 2883u

14)s4

+ 4t3u3(647t

13+ 9737ut

12+ 60783u

2t11

+ 220492u3t10

+ 533350u4t9

+ 931704u5t8

+ 1224463u6t7

+ 1224463u7t6

+ 931704u8t5

+ 533350u9t4

+ 220492u10t3

+ 60783u11t2

+ 9737u12t + 647u

13)s3

+ 3 t4u4(t+ u)

2(961t

10+ 7506ut

9+ 28145u

2t8

+ 66084u3t7

+ 107838u4t6

+ 127716u5t5

+ 107838u6t4

+ 66084u7t3

+ 28145u8t2

+ 7506u9t + 961u

10)s2

+ 6t5u5(t + u)

3(157t

8+ 937u t

7+ 2766u

2t6

+ 5043u3t5

+ 6226u4t4

+ 5043u5t3

+ 2766u6t2

+ 937u7t

+ 157u8)s + t

6u6(t + u)

6(193t

4+ 354ut

3+ 537u

2t2

+ 354 u3t + 193u

4))H(2, y)

}/(27s

3t3u3(s + t)

6(s + u)

6(t + u)

6)

A(2)5;CAnf

=

{216s

2t2u3(s+u)

6(t+u)

6(s2−ts+t

2+u

2)H(0, 1, y) (s+t)

7+162s

2t3u3(s+u)

6(t+u)

6(t2

+u2)H(0, y)H(0, z) (s+t)

6

= + 54s2t2u3(s+u)

6(t+u)

6(16s

3 − 21us2

+ 7u2s+ t

(16t

2 − 21ut+ 7u2))H(0, z)H(1, y)(s+ t)

6 − 54s2t2u3

(s+u)6(t+u)

6(10s

3

− 21us2

+ 19u2s + t

(− 8t

2+ 21ut− 17 u

2))H(0, y)H(1, z)(s + t)

6+ 1134s

2t2u3(s + u)

6(t + u)

6(s3 − 2us

2

+ u2s + t(t− u)

2)H(1, y)H(1, z)(s + t)

6+ 54s

2t2u2(s + u)

6(t + u)

6(− 2(5t + 8u)s

3+ 21

(t2

+ u2)s2 −

(19t

3

+ 7u3)s + tu

(t2

+ u2))H(0, z) H(2, y)(s + t)

6+ 54s

2t2u2(s + u)

6(t + u)

6(− 4(5t + 6u)s

3+ 21

(t2

+ 2u2)s2

−(11t

3+ 24u

3)s + tu

(t2

+ u2))H(1, z)H(2, y)(s + t)

6+ 162s

3t2u2(s + u)

6(t + u)

6(2(t + u)s

2 − 7(t2

+ u2)s + 5

(t3

+ u3))H(1, z)H(3, y)(s + t)

6+ 162s

2t3u3(s + u)

6(t + u)

6(2t

2 − 7ut + 5u2)H(0, 0, y)(s + t)

6

= + 162s2t3u3

(s+u)6(t+u)

6(5t

2 − 7ut+ 2u2)H(0, 0, z)(s+ t)

6+ 54s

2t2u3(s+u)

6(t+u)

6(7s

3 − 21us2

+ 16u2s+ t

(25t

2 − 42ut

+ 25 u2))H(0, 1, z)(s + t)

6+ 54s

2t2u2(s + u)

6(t + u)

6((t− 10u)s

3+ 21u

2s2

+(t3 − 19u

3)s + 21t(t− u)

2u)H(0, 2, y)(s + t)

6

+ 54s2t2u3(s+ u)

6(t+ u)

6(10s

3 − 21u s2

+ 19u2s+ t

3+ tu

2)H(1, 0, y)(s+ t)

6 − 54s2t2u3(s+ u)

6(t+ u)

6(16s

3 − 21us2

+ 7u2s

− 2t(t2

+ u2))

H(1, 0, z)(s + t)6 − 54s

2t2u3(s + u)

6(t + u)

6(s3 − 21us

2+ 10u

2s + t

(t2 − 21ut + 10u

2))H(1, 1, y)(s + t)

6

− 162s2t2u3

(s + u)6(t + u)

6(8s

3 − 14us2

+ 8u2s + t

(− 4t

2+ 7ut− 7 u

2))H(1, 1, z)(s + t)

6+ 1134s

2t2u3(s + u)

6(t + u)

6(s3

− 2us2

+ u2s + t(t− u)

2)H(1, 2, y)(s + t)

6+ 54s

2t2u2

(s + u)6(t + u)

6(− 2(8t + 5u)s

3+ 21

(t2

+ u2)s2 −

(7 t

3

+ 19u3)s + tu

(t2

+ u2))H(2, 0, y)(s + t)

6+ 54s

2t2u3(s + u)

6(t + u)

6(4s

3 − 21us2

+ 13u2s + t

3+ tu

2)H(2, 1, y)(s + t)

6

− 324s3t2u2(s + u)

6(t + u)

6(4(t + u)s

2 − 7(t2

+ u2)s + 4

(t3

+ u3))H(2, 2, y)(s + t)

6+ 162 s

3t2u2(s + u)

6(t + u)

6(2(t + u)s

2

− 7(t2

+u2)s+ 5

(t3

+u3))H(3, 2, y)(s+ t)

6 − 9s2t2u2(t+u)

6(10 s

14+ (60t+ 74u)s

13+ 2(85t

2+ 94ut+ 129u

2)s12

+ 3(100t

3

+74ut2

+123u2t+190u

3)s11

+(360t

4+199u t

3+954u

2t2

+467u3t+900u

4)s10

+(300t

5−194ut4

+4854 u2t3

+635u3t2

+348u4t

+ 1074u5)s9

+ 2(85t

6 − 429u t5

+ 4734u2t4

+ 2414u3t3 − 498u

4t2

+ 135u5t+ 492u

6)s8

+(60t

7 − 874ut6

+ 8919u2t5

+ 5677u3t4

+ 1791u4t3 − 159u

5t2

+ 165u6t+ 678u

7)s7

+(10t

8 − 337ut7

+ 4848u2t6 − 2634 u

3t5

+ 4506u4t4

+ 5835u5t3

+ 288u6t2

+ 39u7t

+ 330u8)s6

+ u(− 36t

8+ 1746ut

7 − 7930u2t6

+ 1614u3t5

+ 14679u4t4

+ 3583u5t3 − 339u

6t2

+ 150u7t+ 100u

8)s5

+ u2(360t

8

=− 4417u t7 − 1014u

2t6

+ 13797u3t5

+ 8278u4t4 − 689u

5t3

+ 306u6t2

+ 172u7t + 14u

8)s4

+ tu3(− 708t

7 − 45ut6

+ 4974u2t5

+6885u3t4

+1171u4t3−108u

5t2

+489u6t+44u

7)s3

+3t2u4(120 t

6+114ut

5+580u

2t4

+562u3t3

+152u4t2

+117u5t+42u

6)s2

+ t3u5(− 36t

5 − 53ut4

+ 526u2t3

+ 402u3t2

+ 271u4t+ 104 u

5)s+ t

4u6(10t

4+ 40ut

3+ 72u

2t2

+ 49u3t+ 56 u

4))H(0, y)(s+ t)

2

+ 9s2t2u2(s + u)

6(t + u)

6(6 s

8+ (78t + 22u)s

7+(324t

2+ 202ut + 42u

2)s6

+ 3(230 t

3+ 202ut

2+ 186u

2t + 7u

3)s5

+(876t

4

+ 962ut3

+ 1710u2t2

+ 103u3t+ 58u

4)s4

+ 2t(345t

4+ 481ut

3+ 1194u

2t2

+ 38 u3t+ 122u

4)s3

+ 2t2(162t

4+ 303ut

3+ 855u

2t2

+ 38u3t+ 162u

4)s2

+ t3(78t

4+ 202ut

3+ 558u

2t2

+ 103u3t+ 244 u

4)s+ t

4(6t

4+ 22ut

3+ 42u

2t2

+ 21u3t+ 58 u

4))H(1, y)(s+ t)

2

– 21 –

=−3

2t2u2(s+ u)

(462(t+ u)

6s16

+ 6(533t

7+ 3647ut

6+ 11355u

2t5

+ 18041u3t4

+ 18041u4t3

+ 11355u5t2

+ 3647u6t+ 533u

7)s15

+6(t+u)2(1725 t

6+9572ut

5+26881u

2t4

+27580u3t3

+26881u4t2

+9572u5t+1725 u

6)s14

+(20814t

9+169590ut

8+698271u

2t7

+1572623u3t6

+2180718u4t5

+2180718u5t4

+1572623u6t3

+698271u7t2

+169590 u8t+20814u

9)s13

+(t+u)2(28872t

8+187896ut

7

+ 702435 u2t6

+ 1379212u3t5

+ 1402562u4t4

+ 1379212u5t3

+ 702435u6t2

+ 187896u7t+ 28872u

8)s12

+(28752t

11+ 247032u t

10

+ 1200159u2t9

+ 3905948u3t8

+ 7929314u4t7

+ 10661099u5t6

+ 10661099u6t5

+ 7929314u7t4

+ 3905948u8t3

+ 1200159u9t2

+ 247032 u10t + 28752u

11)s11

+ (t + u)2(20598t

10+ 137298u t

9+ 671079u

2t8

+ 2337710u3t7

+ 4295427u4t6

+ 4577312u5t5

+ 4295427 u6t4

+ 2337710u7t3

+ 671079u8t2

+ 137298u9t+ 20598u

10)s10

+(10230t

13+ 94398ut

12+ 670143u

2t11

+ 3176397u3t10

+ 9253014u4t9

+ 16795202u5t8

+ 21138216u6t7

+ 21138216u7t6

+ 16795202u8t5

+ 9253014u9t4

+ 3176397u10t3

+ 670143u11

t2

+ 94398u12t + 10230u

13)s9

+ (t + u)2(3174t

12+ 28308u t

11+ 353829u

2t10

+ 1598364u3t9

+ 3798910u4t8

+ 5149552u5t7

+ 4884942u6t6

+ 5149552u7t5

+ 3798910u8t4

+ 1598364u9t3

+ 353829 u10t2

+ 28308u11t + 3174u

12)s8

+(462t

15+ 7482u t

14

+ 190719u2t13

+ 1263290u3t12

+ 4354796u4t11

+ 9652847u5t10

+ 14817008u6t9

+ 17262724u7t8

+ 17262724u8t7

+ 14817008u9t6

+ 9652847u10t5

+ 4354796u11t4

+ 1263290u12t3

+ 190719u13

t2

+ 7482u14t + 462u

15)s7

+ tu(t + u)2(690t

12+ 52407u t

11

=+300320u2t10

+958425u3t9

+2341562u4t8

+3965828u5t7

+4535936u6t6

+3965828u7t5

+2341562u8t4

+958425u9t3

+300320 u10t2

+52407u11t+690u

12)s6

+t2u2(6786 t

13+57592ut

12+322024u

2t11

+1440278u3t10

+4550721u4t9

+9574691u5t8

+13690372u6t7

+ 13690372u7t6

+ 9574691u8t5

+ 4550721u9t4

+ 1440278u10t3

+ 322024u11t2

+ 57592u12t + 6786 u

13)s5

+ t3u3(t + u)

2(74t

10

+ 34768ut9

+ 270574u2t8

+ 947815u3t7

+ 1872940u4t6

+ 2304682u5t5

+ 1872940u6t4

+ 947815 u7t3

+ 270574u8t2

+ 34768u9t

+ 74u10)s4

+ t4u4(t+ u)

3(4432t

8+ 44590ut

7+ 177657u

2t6

+ 382429u3t5

+ 481348u4t4

+ 382429u5t3

+ 177657u6t2

+ 44590u7t

+4432u8)s3

+t5u5

(t+u)4(2948t

6+20395ut

5+53828u

2t4

+72306u3t3

+53828u4t2

+20395u5t+2948u

6)s2

+720t6u6(t+u)

7(2t

2

+3ut+2 u2)s+288t

7u7(t+u)

6(t2

+ut+u2))

(s+t)−9s2t2u2(s+u)

2(t+u)

6(10s

14+(74t+60u)s

13+2(129 t

2+94ut+85u

2)s12

+ 3(190t

3+ 123ut

2+ 74u

2t + 100 u

3)s11

+(900t

4+ 467ut

3+ 954u

2t2

+ 199u3t + 360 u

4)s10

+(1074t

5+ 348ut

4+ 635u

2t3

+ 4854u3t2 − 194u

4t + 300u

5)s9

+ 2(492t

6+ 135ut

5 − 498u2t4

+ 2414u3t3

+ 4734 u4t2 − 429u

5t + 85u

6)s8

+(678t

7+ 165ut

6

− 159u2t5

+ 1791 u3t4

+ 5677u4t3

+ 8919u5t2 − 874u

6t+ 60u

7)s7

+(330 t

8+ 39ut

7+ 288u

2t6

+ 5835u3t5

+ 4506u4t4 − 2634u

5t3

+4848u6t2−337u

7t+10u

8)s6

+ t(100t

8+150ut

7−339u2t6

+3583 u3t5

+14679u4t4

+1614u5t3−7930u

6t2

+1746u7t−36u

8)s5

+ t2(14t

8+172ut

7+306u

2t6−689u

3t5

+8278u4t4

+13797 u5t3−1014u

6t2−4417u

7t+360u

8)s4

+ t3u(44t

7+489u t

6−108u2t5

+1171u3t4

+6885u4t3

+4974u5t2−45u

6t−708 u

7)s3

+3t4u2(42t

6+117ut

5+152u

2t4

+562u3t3

+580 u4t2

+114u5t+120u

6)s2

= + t5u3(104t

5+ 271ut

4+ 402u

2t3

+ 526u3t2 − 53u

4t− 36u

5)s + t

6u4(56t

4+ 49ut

3+ 72 u

2t2

+ 40u3t + 10u

4))H(0, z)

− 9s2t2u2(2(3 t

6+ 60ut

5 − 78u2t4

+ 490u3t3 − 78u

4t2

+ 60u5t+ 3u

6)s16

+(72t

7+ 1289ut

6+ 414u

2t5

+ 8005u3t4

+ 7845u4t3

+126u5t2

+1129u6t+40u

7)s15

+6(60t

8+900ut

7+1076u

2t6

+4412u3t5

+9687u4t4

+3894u5t3

+558u6t2

+678u7t+23 u

8)s14

+(1024t

9+ 12954ut

8+ 24576u

2t7

+ 46761u3t6

+ 163314u4t5

+ 154677u5t4

+ 29274u6t3

+ 11781u7t2

+ 8316u8t + 331 u

9)s13

+(1874t

10+ 20222ut

9+ 53220u

2t8

+ 61201u3t7

+ 246846u4t6

+ 451965u5t5

+ 210152u6t4

+ 17091u7t3

+ 26370u8t2

+ 11421u9t

+ 638u10)s12

+ 3(780t

11+ 7249u t

10+ 25014u

2t9

+ 30013u3t8

+ 86909u4t7

+ 276042u5t6

+ 269826u6t5

+ 71475u7t4

+ 13798u8t3

+ 15298u9t2

+ 4109u10t + 359 u

11)s11

+(2042t

12+ 16125ut

11+ 76122u

2t10

+ 155760u3t9

+ 296460u4t8

+ 1068120u5t7

+ 1786074u6t6

+ 1133742 u7t5

+ 352110u8t4

+ 166875u9t3

+ 68808u10t2

+ 12114u11t + 1520 u

12)s10

+(1240t

13+ 7152ut

12

+58566u2t11

+232980 u3t10

+464512u4t9

+1090308u5t8

+2341921u6t7

+2520886u7t6

+1455108u8t5

+740077u9t4

+345463u10t3

+84624u11t2

+10790 u12t+1573u

13)s9

+3(168t

14+208ut

13+10592u

2t12

+73981u3t11

+192464u4t10

+350678u5t9

+731518u6t8

– 22 –

= + 1095507u7t7

+ 938868u8t6

+ 596751u9t5

+ 345880u10t4

+ 133260 u11t3

+ 25570u12t2

+ 2627u13t + 352u

14)s8

+(124 t

15

−1050ut14

+11760u2t13

+109681u3t12

+348969u4t11

+744780u5t10

+1812415u6t9

+3571941u7t8

+4045692u8t7

+2838503u9t6

+1635744u10t5

+818670u11t4

+274406u12t3

+50556u13t2

+4374u14t+403u

15)s7

+(14t

16−459 ut15

+4194u2t14

+16667u3t13

+ 21936u4t12

+ 169446u5t11

+ 1113116u6t10

+ 3298442u7t9

+ 4969926u8t8

+ 4145565u9t7

+ 2172862u10t6

+ 899067u11t5

+ 350974u12t4

+ 118004u13

t3

+ 24360u14t2

+ 1596u15t + 66u

16)s6

+ 3tu(− 20 t

15+ 510ut

14 − 2846u2t13 − 25726u

3t12

−36057u4t11

+137862 u5t10

+687022u6t9

+1363652u7t8

+1488125u8t7

+962136u9t6

+387285u10t5

+104624u11t4

+27898u12t3

+ 10766u13

t2

+ 2505u14t + 88u

15)s5

+ t2u2(276t

14 − 4915u t13 − 35832u

2t12 − 60573u

3t11

+ 131822u4t10

+ 839823u5t9

+ 1989780u6t8

+ 2753037u7t7

+ 2394378u8t6

+ 1355826u9t5

+ 497554 u10t4

+ 108936u11t3

+ 16362u12t2

+ 4782u13t+ 1056 u

14)s4

+ t3u3(− 820t

13 − 4665ut12 − 3330u

2t11

+ 50014u3t10

+ 234315u4t9

+ 583398u5t8

+ 954377u6t7

+ 1055745 u7t6

+ 809880u8t5

+ 443150u9t4

+ 168838u10t3

+ 40614u11

t2

+ 5192u12t + 196u

13)s3

+ 3t4u4(t + u)

2(92 t

10+ 476ut

9+ 2090u

2t8

+ 7269u3t7

+ 17036u4t6

+ 25733u5t5

+ 22780 u6t4

+ 14183u7t3

+ 6446u8t2

+ 2047u9t+ 352u

10)s2 − t5u5

(t+ u)3(60t

8+ 29ut

7 − 1449u2t6

−4932u3t5−8177u

4t4−6609 u

5t3−3504u

6t2−1214u

7t−264u

8)s+t

6u6(t+u)

6(14 t

4+90ut

3+126u

2t2

+89u3t+66u

4))H(1, z)

=− 9s2t2u2(2(6t

6+ 78ut

5 − 33u2t4

+ 550u3t3 − 33u

4t2

+ 78u5t + 6 u

6)s16

+(130t

7+ 1727ut

6+ 1824u

2t5

+ 10515u3t4

+ 10515 u4t3

+ 1824u5t2

+ 1727u6t + 130u

7)s15

+ 6(104t

8+ 1295u t

7+ 2603u

2t6

+ 7743u3t5

+ 14182u4t4

+ 7743u5t3

+ 2603u6t2

+ 1295 u7t + 104u

8)s14

+(1747t

9+ 20760ut

8+ 60177u

2t7

+ 138345 u3t6

+ 311235u4t5

+ 311235u5t4

+ 138345u6t3

+ 60177u7t2

+ 20760u8t + 1747u

9)s13

+(3218t

10+ 37773ut

9+ 146652u

2t8

+ 339358 u3t7

+ 769808u4t6

+ 1107894u5t5

+ 769808u6t4

+ 339358u7t3

+ 146652 u8t2

+ 37773u9t + 3218u

10)s12

+ 3(1403t

11+ 16697u t

10+ 82856u

2t9

+ 227499u3t8

+ 514057u4t7

+ 898468u5t6

+ 898468u6t5

+ 514057u7t4

+ 227499u8t3

+ 82856u9t2

+ 16697u10t + 1403 u

11)s11

+ 2(2050t

12

+ 24939ut11

+ 154530u2t10

+ 531155u3t9

+ 1271385u4t8

+ 2420490u5t7

+ 3112438u6t6

+ 2420490u7t5

+ 1271385u8t4

+ 531155u9t3

+ 154530u10t2

+ 24939 u11t+ 2050u

12)s10

+(2989t

13+ 37142ut

12+ 287298 u

2t11

+ 1240898u3t10

+ 3321201u4t9

+ 6609462u5t8

+ 9856850u6t7

+ 9856850u7t6

+ 6609462u8t5

+ 3321201u9t4

+ 1240898u10

t3

+ 287298u11t2

+ 37142u12t

+ 2989u13)s9

+ 3(514 t

14+ 6775ut

13+ 65664u

2t12

+ 346961u3t11

+ 1076100u4t10

+ 2314869u5t9

+ 3821756u6t8

+ 4598458u7t7

+ 3821756u8t6

+ 2314869u9t5

+ 1076100u10t4

+ 346961u11t3

+ 65664u12

t2

+ 6775u13t + 514u

14)s8

+(493t

15+ 8076ut

14

+ 98952 u2t13

+ 596673u3t12

+ 2146416u4t11

+ 5342982u5t10

+ 10174467 u6t9

+ 14554545u7t8

+ 14554545u8t7

+ 10174467u9t6

+ 5342982u10

t5

+ 2146416u11t4

+ 596673u12t3

+ 98952u13t2

+ 8076u14t + 493 u

15)s7

+(72t

16+ 2194ut

15+ 36630u

2t14

= + 227075u3t13

+ 910630u4t12

+ 2784993u5t11

+ 6611664u6t10

+ 11660494u7t9

+ 14240640u8t8

+ 11660494u9t7

+ 6611664u10t6

+ 2784993u11

t5

+ 910630u12t4

+ 227075u13t3

+ 36630u14t2

+ 2194u15t + 72 u

16)s6

+ 3tu(100t

15+ 3071ut

14+ 18464u

2t13

+ 80084u3t12

+ 323267u4t11

+ 1009711u5t10

+ 2219756u6t9

+ 3327843u7t8

+ 3327843u8t7

+ 2219756u9t6

+ 1009711u10

t5

+ 323267u11t4

+ 80084u12t3

+ 18464u13t2

+ 3071u14t + 100 u

15)s5

+ t2u2(1146t

14+ 7452ut

13+ 43332u

2t12

+ 256857u3t11

+ 1020516u4t10

+ 2637270u5t9

+ 4640688u6t8

+ 5609726u7t7

+ 4640688u8t6

+ 2637270u9t5

+ 1020516u10

t4

+ 256857u11t3

+ 43332u12t2

+ 7452u13t + 1146u

14)s4

+ t3u3(316t

13+ 7702ut

12+ 60600u

2t11

+ 260422u3t10

+ 721307u4t9

+ 1402338u5t8

+ 1962295u6t7

+ 1962295u7t6

+ 1402338u8t5

+ 721307u9t4

+ 260422u10t3

+ 60600u11t2

+ 7702 u12t + 316u

13)s3

+ 3t4u4(t + u)

2(382t

10+ 2457u t

9+ 8650u

2t8

+ 21232u3t7

+ 37622u4t6

+ 46842u5t5

+ 37622u6t4

+ 21232u7t3

+ 8650u8t2

+ 2457u9t + 382u

10)s2

+ t5u5

(t + u)3(300t

8+ 1544ut

7+ 4776u

2t6

+ 9573u3t5

+ 12690u4t4

+ 9573u5t3

+ 4776u6t2

+ 1544u7t + 300u

8)s + 3t

6u6(t + u)

6(24t

4+ 37ut

3+ 56u

2t2

+ 37u3t + 24u

4))H(2, y)

}/(27s

3t3u3(s + t)

6(s + u)

6(t + u)

6)

A(2)5;CF nf

=

{− 432s

2t2(s2 − ts + t

2)u3(s + u)

6(t + u)

6H(0, z)H(1, y) (s + t)

7 − 324s2t2u3(s + u)

6(t + u)

6(s2 − ts

= + t2

+ u2)H(1, y) H(1, z)(s + t)

7 − 108s2t2u3(s + u)

6(t + u)

6(s2 − ts + t

2 − 3 u2)H(1, 1, y)(s + t)

7

− 324s2t2u3(s + u)

6(t + u)

6(s2 − t s + t

2+ u

2)H(1, 2, y)(s + t)

7+ 108s

2t3u3(s + u)

6(t + u)

6(t2

+ u2)H(0, y)H(0, z)(s + t)

6

+ 432s2(s− t)t2u5

(s + u)6

(t + u)6H(0, y)H(1, z)(s + t)

6+ 432s

3t2u2(s + u)

6(t + u)

6(t3

+ s2u)H(0, z)H(2, y)(s + t)

6

– 23 –

=+108s3t2u2(s+u)

6(t+u)

6(3 u

3+s

2(4t+3u)

)H(1, z)H(2, y)(s+t)

6−432s3t2u2(s+u)

6(t+u)

7(t2−ut+u2

)H(1, z)H(3, y)(s+t)

6

−432s2t3u5

(s+u)6(t+u)

6H(0, 0, y)(s+ t)

6−432s2t5u3(s+u)

6(t+u)

6H(0, 0, z) (s+ t)

6−108s2t2u3(s+u)

6(t+u)

6(3t

3+3u

2t

+ 4su2)H(0, 1, z)(s + t)

6+ 108s

2t2u3(s + u)

6(t + u)

6(− 3t

3 − 3u2t + 4s u

2)H(0, 2, y)(s + t)

6+ 108s

2t2u3(s + u)

6(t + u)

6(t3

+ u2t− 4su

2)H(1, 0, y)(s+ t)

6+ 108s

2t2u3(s+ u)

6(t+ u)

6(4 s

3+ t

3+ tu

2)H(1, 0, z)(s+ t)

6+ 108s

2t2u3(s+ u)

6(t+ u)

6(3s

3

+ 3u2s− 4tu

2)H(1, 1, z)(s + t)

6+ 432s

3t2u2(s + u)

6(t + u)

6(u3

+ s2t)H(2, 0, y)(s + t)

6+ 108s

3t2u3(s + u)

6(t + u)

6(s2

− 3u2)H(2, 1, y)(s+ t)

6+ 324s

3t2u2(s+ u)

6(t+ u)

7(s2

+ t2

+ u2 − tu

)H(2, 2, y)(s+ t)

6 − 432s3t2u2

(s+ u)6(t+ u)

7(t2 − ut

+u2)H(3, 2, y)(s+ t)

6− 18s2t2u3

(s+u)6(t+u)

6(9(t+ 2u)s

4+ 9(3t

2+ 6ut+ 2u

2)s3

+(27t

3+ 72ut

2+ 12u

2t+ 16u

3)s2

+ t(9t

3

+ 54u t2

+ 12u2t+ 20u

3)s+ 2t

2u(9t

2+ 9ut+ 8u

2))

H(1, y)(s+ t)4 − 18s

2t3u3(t+ u)

6(18s

11+ 51(t+ 2u) s

10+(33t

2+ 360ut

+203u2)s9

+(−27t

3+498ut

2+705 u

2t+156u

3)s8

+(−39t

4+420ut

3+776u

2t2

+546u3t−63 u

4)s7−3

(4t

5−108ut4−91u

2t3

=−106u3t2

+21u4t+98 u

5)s6−3u

(−64t

5−9ut4

+98u2t3

+142u3t2

+236u4t+121u

5)s5−u

(−48t

6−44ut5

+174u2t4

+711u3t3

+1102 u4t2

+897u5t+240u

6)s4−u2

(−16t

6−100ut5

+333u2t4

+948u3t3

+1084u4t2

+558u5t+83u

6)s3−3u

3(−16 t

6+8ut

5

+ 124u2t4

+ 199u3t3

+ 182u4t2

+ 60u5t+ 4u

6)s2 − t u5

(52t

4+ 135ut

3+ 186u

2t2

+ 147u3t+ 24u

4)s− 2t

2u6(4t

3+ 9ut

2+ 13u

2t

+ 8u3))H(0, y)(s+ t)

3 − 12t3u3

(s+ u)(24tu

(3t

3+ 4ut

2+ 4u

2t+ 3u

3)s15 − 6(t+ u)

2(19t

4 − 7ut3

+ 86u2t2 − 7u

3t+ 19u

4)s14

−(528 t

7+2241ut

6+5905u

2t5

+10806u3t4

+10806u4t3

+5905u5t2

+2241 u6t+528u

7)s13−(t+u)

2(999t

6+3708ut

5+7757u

2t4

+13636u3t3

+7757u4t2

+3708u5t+999u

6)s12−

(945 t

9+6444ut

8+18478u

2t7

+38524u3t6

+60985u4t5

+60985u5t4

+38524 u6t3

+18478u7t2

+6444u8t+945u

9)s11− (t+u)

2(408 t

8+1419ut

7−737u2t6−1221u

3t5

+6934u4t4−1221u

5t3−737u

6t2

+1419u7t

+ 408u8)s10

+ 2(− 9t

11+ 1365ut

10+ 9543 u

2t9

+ 28308u3t8

+ 43963u4t7

+ 44166u5t6

+ 44166u6t5

+ 43963u7t4

+ 28308u8t3

+ 9543u9t2

+ 1365u10t− 9u

11)s9

+ (t + u)2(33t

10+ 3726ut

9+ 16908u

2t8

+ 31720u3t7

+ 24859u4t6

+ 8028 u5t5

+ 24859u6t4

+ 31720u7t3

+ 16908u8t2

+ 3726u9t + 33 u

10)s8

+(3t

13+ 2076ut

12+ 13514u

2t11

+ 34430u3t10

+ 33548u4t9 − 29287u

5t8

− 114020u6t7 − 114020u

7t6 − 29287u

8t5

+ 33548u9t4

+ 34430u10t3

+ 13514u11t2

+ 2076u12t + 3 u

13)s7

+ tu(t + u)2(615t

10

= + 2129ut9 − 2862u

2t8 − 27958 u

3t7 − 70915u

4t6 − 96406u

5t5 − 70915u

6t4 − 27958u

7t3 − 2862u

8t2

+ 2129u9t + 615u

10)s6

+tu(87t

13+151ut

12−4613 u2t11−33895u

3t10−117246u

4t9−252106u

5t8−365426u

6t7−365426u

7t6−252106u

8t5−117246u

9t4

−33895u10t3−4613 u

11t2

+151u12t+87u

13)s5− t2u2

(t+u)2(61 t

10+1421ut

9+9539u

2t8

+31118u3t7

+60284u4t6

+74918u5t5

+ 60284u6t4

+ 31118u7t3

+ 9539u8t2

+ 1421u9t+ 61u

10)s4 − t3u3

(t+u)3(119t

8+ 1631ut

7+ 6699u

2t6

+ 14006u3t5

+ 17750u4t4

+14006u5t3

+6699u6t2

+1631u7t+119u

8)s3−t4u4

(t+u)4(133t

6+842ut

5+1972u

2t4

+2532u3t3

+1972 u4t2

+842u5t+133u

6)s2

−6t5u5(t+u)

7(8t

2+9ut+8 u

2)s−6t

6u6(t+u)

6(t2

+ut+u2))

(s+ t)−18s2t3u3(s+u)

3(t+u)

6(18s

11+51(2t+u)s

10+(203t

2

+360 ut+33u2)s9

+3(52t

3+235ut

2+166u

2t−9u

3)s8

+(−63t

4+546ut

3+776u

2t2

+420u3t−39u

4)s7−3

(98t

5+21ut

4−106u2t3

− 91u3t2 − 108u

4t+ 4u

5)s6 − 3t

(121t

5+ 236ut

4+ 142u

2t3

+ 98u3t2 − 9u

4t− 64u

5)s5 − t

(240t

6+ 897ut

5+ 1102u

2t4

+ 711u3t3

+174u4t2−44u

5t−48 u

6)s4− t2

(83t

6+558ut

5+1084u

2t4

+948u3t3

+333u4t2−100u

5t−16u

6)s3−3t

3(4t

6+60ut

5+182u

2t4

+199 u3t3

+124u4t2

+8u5t−16u

6)s2−t5u

(24t

4+147u t

3+186u

2t2

+135u3t+52u

4)s−2t

6u2(8t

3+13ut

2+9 u

2t+4u

3))H(0, z)

= + 18s2t2u3(16t

2u(3t

2+ u t+ 3u

2)s16 − 4t

(t5 − 96ut

4 − 125u2t3 − 125u

3t2 − 96u

4t+ u

5)s15

+ 3(− 21t

7+ 376ut

6+ 969u

2t5

+ 1014u3t4

+ 1053 u4t3

+ 460u5t2

+ 15u6t + 6u

7)s14

+ 3(− 91t

8+ 434u t

7+ 2445u

2t6

+ 3548u3t5

+ 4121u4t4

+ 3594u5t3

+ 1259u6t2

+ 200u7t + 42u

8)s13

+(− 507t

9 − 228ut8

+ 8958u2t7

+ 21034u3t6

+ 29016u4t5

+ 37554u5t4

+ 27842u6t3

+ 10398u7t2

+ 2643u8t + 394 u

9)s12

+ 3(− 139t

10 − 658ut9

+ 1402u2t8

+ 7968u3t7

+ 14642u4t6

+ 25576u5t5

+ 31288u6t4

+ 20652u7t3

+ 8197u8t2

+ 2094u9t + 242u

10)s11

+(− 33t

11 − 1944ut10 − 2626 u

2t9

+ 15924u3t8

+ 52455u4t7

+ 115368u5t6

+ 193671u6t5

+ 189594u7t4

+ 109994u8t3

+ 41340u9t2

+ 9291u10t+ 870u

11)s10

+(229t

12 − 1206ut11 − 7826u

2t10

+ 2016u3t9

+ 60801u4t8

+ 168742u5t7

+ 312211u6t6

+ 377892u7t5

+ 285136u8t4

+ 142036u9t3

+ 47343u10t2

+ 9112u11t + 698u

12)s9

+ 3(69 t

13 − 396ut12 − 3542u

2t11 − 3876u

3t10

+ 19403u4t9

+ 74332u5t8

+ 145298u6t7

+ 193458u7t6

+ 172121u8t5

+ 103198u9t4

+ 43468u10t3

+ 12394u11t2

+ 2015u12t+ 122u

13)s8

+(81 t

14 − 1338ut13 − 9602u

2t12 − 15144u

3t11

+ 41583u4t10

+ 217006u5t9

+ 472374u6t8

+ 692016u7t7

+ 711667u8t6

+ 501642 u9t5

+ 246150u10t4

+ 85492u11t3

+ 19953u12t2

+ 2646u13

t + 114u14)s7

– 24 –

= +(12t

15− 936ut14− 5785u

2t13− 9734 u

3t12

+ 23766u4t11

+ 151768u5t10

+ 374411u6t9

+ 611526u7t8

+ 725603u8t7

+ 609872u9t6

+355422u10t5

+143724u11t4

+39635 u12t3

+7044u13t2

+696u14t+16u

15)s6

+3tu(−112t

14−711ut13−1428u

2t12

+2680u3t11

+24408u4t10

+73333u5t9

+137580u6t8

+184601u7t7

+179614u8t6

+124026u9t5

+59992u10t4

+19831u11t3

+4174u12t2

+496u13t

+28 u14)s5

+ t2u(−48t

14−380ut13−1422u

2t12−453 u

3t11

+19778u4t10

+90336u5t9

+213354u6t8

+330336u7t7

+360906u8t6

+281670u9t5

+156716u10t4

+61605u11t3

+16236 u12t2

+2470u13t+144u

14)s4

+t3u2(−16t

13−340 ut12−1209u

2t11

+1822u3t10

+23522u4t9

+76164u5t8

+142722 u6t7

+179964u7t6

+159444u8t5

+99732u9t4

+43795u10t3

+13194 u11t2

+2510u12t+232u

13)s3

− 3t4u3(t + u)

2(16 t

10+ 56ut

9 − 124u2t8 − 1147u

3t7 − 3208u

4t6 − 5170u

5t5 − 5528u

6t4 − 3835u

7t3 − 1676u

8t2 − 424u

9t

− 48u10)s2

+ t5u5(t+ u)

3(52t

7+ 321ut

6+ 921u

2t5

+ 1569u3t4

+ 1779u4t3

+ 1230u5t2

+ 484u6t+ 84u

7)s+ 2t

6u6(t+ u)

7(4t

2

+ 5ut+ 8 u2))H(1, z) + 18s

2t2u2(16t

2u2(3t

2+ ut+ 3 u

2)s16 − 4tu

(t5 − 96ut

4 − 125u2t3 − 125u

3t2 − 96u

4t+ u

5)s15

+ 6(3t

8

+ 9ut7

+ 242u2t6

+ 567u3t5

+ 582u4t4

+ 567u5t3

+ 242u6t2

+ 9u7t + 3u

8)s14

+ 3(42t

9+ 221u t

8+ 1445u

2t7

+ 4311u3t6

+ 5693u4t5

+ 5693u5t4

+ 4311u6t3

+ 1445 u7t2

+ 221u8t+ 42u

9)s13

+ 2(197t

10+ 1416ut

9+ 6153 u

2t8

+ 18148u3t7

+ 29594u4t6

+ 32160u5t5

+ 29594u6t4

+ 18148u7t3

+ 6153u8t2

+ 1416u9t + 197u

10)s12

+ 3(242t

11+ 2199 ut

10+ 9451u

2t9

+ 27134u3t8

= + 50612u4t7

+ 62634u5t6

+ 62634u6t5

+ 50612u7t4

+ 27134u8t3

+ 9451u9t2

+ 2199u10t + 242u

11)s11

+ 2(435t

12+ 4803ut

11

+ 23010u2t10

+ 69466u3t9

+ 145491u4t8

+ 210555u5t7

+ 230976u6t6

+ 210555u7t5

+ 145491u8t4

+ 69466u9t3

+ 23010u10t2

+4803u11t+435u

12)s10

+(698t

13+9301ut

12+51105u

2t11

+170974u3t10

+406704u4t9

+698997u5t8

+884941u6t7

+884941u7t6

+ 698997 u8t5

+ 406704u9t4

+ 170974u10t3

+ 51105u11t2

+ 9301u12t+ 698 u

13)s9

+ 6(61t

14+ 1018ut

13+ 6515u

2t12

+ 24975u3t11

+ 68497u4t10

+ 139578u5t9

+ 209143u6t8

+ 237090u7t7

+ 209143 u8t6

+ 139578u9t5

+ 68497u10t4

+ 24975u11t3

+ 6515u12

t2

+1018u13t+61u

14)s8

+(114t

15+2655ut

14+20511 u

2t13

+93946u3t12

+304122u4t11

+729081u5t10

+1284397u6t9

+1678662u7t8

+1678662u8t7

+1284397u9t6

+729081u10t5

+304122 u11t4

+93946u12t3

+20511u13t2

+2655u14t+114u

15)s7

+2(8t

16+348ut

15

+ 3558u2t14

+ 20893u3t13

+ 82679u4t12

+ 233298u5t11

+ 478228u6t10

+ 720901u7t9

+ 821694u8t8

+ 720901u9t7

+ 478228u10t6

+ 233298u11t5

+ 82679u12

t4

+ 20893u13t3

+ 3558u14t2

+ 348u15t + 8u

16)s6

+ 3tu(28t

15+ 496ut

14+ 4255u

2t13

+ 21403u3t12

= + 71760u4t11

+ 172018u5t10

+ 302499u6t9

+ 397333u7t8

+ 397333u8t7

+ 302499 u9t6

+ 172018u10t5

+ 71760u11t4

+ 21403u12t3

+4255u13t2

+496u14t+28u

15)s5

+2t2u2(72t

14+1235u t

13+8343u

2t12

+34020u3t11

+97435u4t10

+204801u5t9

+317982u6t8

+367512u7t7

+317982u8t6

+204801u9t5

+97435u10t4

+34020u11t3

+8343u12t2

+1235u13t+72u

14)s4

+t3u3(232t

13+2510ut

12

+ 13689u2t11

+ 49393u3t10

+ 127070 u4t9

+ 236640u5t8

+ 321522u6t7

+ 321522u7t6

+ 236640u8t5

+ 127070 u9t4

+ 49393u10t3

+ 13689u11t2

+ 2510u12t+ 232u

13)s3

+ 6t4u4(t+ u)

2(24t

10+ 212ut

9+ 892u

2t8

+ 2315u3t7

+ 4004u4t6

+ 4762u5t5

+ 4004u6t4

+2315u7t3

+892u8t2

+212u9t+24u

10)s2

+ t5u5(t+u)

3(84t

8+484ut

7+1347u

2t6

+2364u3t5

+2802u4t4

+2364u5t3

+1347u6t2

+ 484u7t + 84 u

8)s + 2t

6u6(t + u)

6(8t

4+ 13ut

3+ 18u

2t2

+ 13u3t + 8 u

4))H(2, y)

}/(27s

3t3u3(s + t)

6(s + u)

6(t + u)

6)

A(2)

5;n2f

= 2

{t3uH(2, y) + t

3uH(1, z)− tu

(t2

+ u2)H(0, y)− tu

(t2

+ u2)H(0, z) + tu

3H(2, y) + t u

3H(1, z)

+ s4

+ 2s3t + 2s

3u + 3s

2t2

+ 3s2u2

+ 2st3

+ 2su3

+ t4

+ 2t3u + 3t

2u2

+ 2tu3

+ u4

}/(3stu

)

A(2)

6;C2A

=

{3s

2t2(s+ t)

6u2(t+u)

2((

363t4

+ 492ut3

+ 504u2t2

+ 492 u3t+ 363u

4)s4

+ 2(363t

5+ 479ut

4− 58u2t3− 58u

3t2

+ 479 u4t

= + 363u5)s3

+ 9(t + u)2(121t

4 − 10ut3 − 134u

2t2 − 10u

3t + 121u

4)s2

+ 6(t + u)3(121t

4+ 35ut

3+ 12u

2t2

+ 35u3t + 121u

4)s

+363(t+u)4(t2

+ut+u2)2)

H(1, z) H(2, y)(s+u)6

+3s2t2(s+t)

2u2(t+u)

6(363s

8+726(3t+u)s

7+3

(2057t

2+796ut+363u

2)s6

+ 6(1815t

3+ 480ut

2+ 348u

2t+ 121u

3)s5

+(13068t

4+ 1782ut

3− 297u2t2

+ 958u3t+ 363 u

4)s4

+ 2t(5445t

4+ 891ut

3− 1296u2t2

−58u3t+246 u

4)s3

+ t2(6171t

4+2880ut

3−297u2t2−116u

3t+504 u

4)s2

+2t3(1089t

4+1194ut

3+1044u

2t2

+479u3t+246 u

4)s

+ 363t4(t2

+ ut+ u2)2)

H(0, 0, y)(s+ u)6

+ 36 s2t2(s+ t)

2u2(t+ u)

6(22s

8+ 44(3t+ u)s

7+ 2(187t

2+ 70u t+ 33u

2)s6

+(660t

3

+ 147ut2

+ 246u2t + 44u

3)s5

+(792t

4+ 41ut

3+ 360u

2t2

+ 115u3t + 22u

4)s4

+ t(660t

4+ 2ut

3+ 246u

2t2

+ 95u3t + 64u

4)s3

+ t2(374 t

4+ 54ut

3+ 84u

2t2

+ 9u3t+ 84u

4)s2

+ t3(132t

4+ 63u t

3+ 36u

2t2− 11u

3t+ 54u

4)s+ t

4(22t

4+ 21ut

3+ 18u

2t2

+ 4u3t

+ 18u4))H(0, z)H(0, 0, y)(s+ u)

6 − 36s2t2(s+ t)

2u2(t+ u)

6(22s

8+ 3(44t+ 7u)s

7+(374t

2+ 63ut+ 18u

2)s6

+(660t

3+ 54ut

2

+ 36u2t+ 4u

3)s5

+(792t

4+ 2u t

3+ 84u

2t2− 11u

3t+ 18u

4)s4

+ t(660t

4+ 41ut

3+ 246u

2t2

+ 9u3t+ 54u

4)s3

+ t2(374t

4+ 147ut

3

+ 360u2t2

+ 95u3t+ 84u

4)s2

+ t3(132t

4+ 140ut

3+ 246u

2t2

+ 115u3t+ 64 u

4)s+ 22t

4(t2

+ut+u2)2)

H(1, z)H(0, 0, y) (s+u)6

– 25 –

= + 108s2t2(s + t)

6u2(t + u)

6(2s

4+ 4(t + u)s

3+ 6

(t2

+ u2)s2

+ 4(t3

+ u3)s + 2t

4+ 2u

4 − 2tu3 − 3t

2u2

− 2t3u)H(0, 0, y)H(0, 0, z)(s+ u)

6+ 18s

2t2(s+ t)

6u2(t+ u)

2((

44t4

+ 296ut3

+ 486u2t2

+ 316u3t+ 58u

4)s4

+ 2(15t

5+ 247ut

4

+634u2t3

+646u3t2

+271u4t+27u

5)s3

+3 (t+u)2(5t

4+150ut

3+228u

2t2

+146u3t+15u

4)s2−2 (t+u)

3(2t

4−91ut3−90u

2t2

− 97u3t− 4u

4)s + (t + u)

4(11t

4+ 94ut

3+ 105u

2t2

+ 72u3t + 6u

4))H(3, y) H(0, 1, z)(s + u)

6 − 108s2t2(s + t)

6u2(t + u)

6(2s

4

+ 2(2t + u)s3

+ 3(2t

2+ u

2)s2

+ 2(2t

3+ u

3)s + 2

(t4 − 2ut

3+ 6 u

2t2

+ u4))H(0, 0, y)H(0, 1, z)(s + u)

6

= + 36s2t2(s + t)

6u2

(t + u)2(2(11t

4+ 32ut

3+ 42u

2t2

+ 27u3t + 9u

4)s4

+(44t

5+ 115ut

4+ 95u

2t3

+ 9u3t2 − 11u

4t

+ 4u5)s3

+ 6 (t + u)2(11t

4+ 19ut

3+ 11u

2t2

+ 3u4)s2

+ (t + u)3(44 t

4+ 8ut

3 − 9u2t2

+ 21u4)s + 22(t + u)

4(t2

+ u t

+ u2)2)

H(1, z)H(0, 2, y)(s+ u)6 − 108s

2t2(s+ t)

6u2

(t+ u)6(2s

4+ 2(t+ 2u)s

3+ 3(t2

+ 2u2)s2

+ 2(t3

+ 2 u3)s+ 2

(t4

+ 6u2t2

−2u3t+u

4))H(0, 0, z) H(0, 2, y)(s+u)

6+108s

2t2(s+t)

6u2(t+u)

6(−2(t−2u)s

3−3(t2−2u

2)s2−2

(t3−2u

3)s+12tu

(t2−u t

+u2))H(0, 1, z)H(0, 2, y)(s+u)

6+216s

2t2(s+t)

6u2

(t+u)6(s4

+2us3

+3u2s2

+2u3s+(t2

+u t+u2)2)

H(0, 1, z)H(0, 3, y)(s+u)6

+18s2t2(s+t)

3u2

(t+u)6(3s

7+(6u−9t)s

6+(−48t

2+12ut+15u

2)s5−(56t

3+6ut

2+63u

2t−12u

3)s4−t2

(7t

2+36u t+222u

2)s3

+ 3t(11t

4 − 14ut3 − 70u

2t2 − 8u

3t− 8 u

4)s2

+ t2(28t

4 − 24ut3 − 81u

2t2 − 24u

3t− 30u

4)s + t

3(8t

4 − 6ut3 − 15u

2t2 − 12u

3t

=− 14u4))H(0, z) H(1, 0, y)(s+u)

6− 18s2t2(s+ t)

3u2(t+u)

6(8s

7+ (28t− 6u)s

6+ 3

(11t

2− 8ut− 5u2)s5−

(7t

3+ 42ut

2+ 81u

2t

+12 u3)s4−2

(28t

4+18ut

3+105u

2t2

+12u3t+7u

4)s3−6t

(8t

4+ut

3+37u

2t2

+4u3t+5u

4)s2−3

(3 t

6−4ut5

+21u2t4

+8u4t2)s

+3t4(t3

+2ut2

+5u2t+4 u

3))H(1, z)H(1, 0, y)(s+u)

6+108s

2t2(s+t)

6u2(t+u)

6(2s

4+2(2t+u)s

3+3(2t

2+u

2)s2

+2(2 t

3+u

3)s

+ 2t4

+ 2u4− 2tu

3+ 9t

2u2− 6t

3u)H(0, 1, z) H(1, 0, y)(s+u)

6− 18s2t2(s+ t)

6u2(t+u)

3(2t(7t

2+ 15u t+ 12u

2)s4

+ 12(t4

+ 2ut3

+2u2t2−u4

)s3

+3(t+u)2(5t

3+17ut

2+31u

2t−5u

3)s2

+6(t+u)3(t3

+ut2

+u2t−u3

)s− (t+u)

3(8t

4+4ut

3−3u2t2−18u

3t

+ 3 u4))H(3, y)H(1, 0, z)(s+u)

6− 108s2t2(s+ t)

6u2(t+u)

6(2s

4+ 4(t−u)s

3+ 6(t2

+ 2u2)s2

+ 4t3s+ 2t

4+ 2u

4+ 2t u

3+ 3t

2u2

+2t3u)H(0, 0, y)H(1, 0, z)(s+u)

6−216s3t2(s+ t)

6u2(t+u)

6(2(t−2u)s

2+3(t2

+u2)s+2

(t3−u3

))H(0, 2, y)H(1, 0, z)(s+u)

6

+ 108s2t2(s+ t)

6u2(t+ u)

6(2s

4+ 2(t+ 3u)s

3+ 3

(t2 − u2

)s2

+ 2(t3

+ 5u3)s+ 2

(t2

+ ut+ u2)2)

H(0, 3, y) H(1, 0, z)(s+ u)6

= + 108s2t2(s + t)

6u2(t + u)

6(2s

4+ (4t− 6u) s

3+(6t

2+ 9u

2)s2

+(4t

3 − 2u3)s + 2t

4+ 2u

4+ 2t u

3+ 3t

2u2

+ 2t3u)H(1, 0, y)H(1, 0, z)(s+u)

6+ 3s

2t2(s+ t)

6u2

(t+u)2((

363t4

+ 492ut3

+ 504u2t2

+ 492u3t+ 363u

4)s4

+ 2(363t

5+ 479ut

4

−58u2t3−58u

3t2

+479u4t+363u

5)s3

+9(t+u)2(121t

4−10ut3−134u

2t2−10u

3t+121u

4)s2

+6(t+u)3(121t

4+35ut

3+12u

2t2

+ 35u3t+ 121u

4)s+ 363(t+ u)

4(t2

+ ut+ u2)2)

H(1, 1, z)(s+ u)6

+ 36s2t2

(s+ t)6u2(t+ u)

2(2(11t

4+ 32ut

3+ 42u

2t2

+ 27u3t

+ 9 u4)s4

+(44t

5+ 115ut

4+ 95u

2t3

+ 9u3t2−11u

4t+ 4 u

5)s3

+ 6(t+u)2(11t

4+ 19ut

3+ 11u

2t2

+ 3u4)s2

+ (t+u)3(44t

4+ 8ut

3

−9u2t2

+21u4)s+22(t+u)

4(t2

+ut+u2)2)

H(0, y)H(1, 1, z)(s+u)6−36s

2t2(s+t)

6u2(t+u)

2(2(20t

4+59ut

3+84u

2t2

+59u3t

+20u4)s4

+8(6t

5+13ut

4+13u

2t3

+13u3t2

+13u4t+6u

5)s3

+6 (t+u)2(14t

4+19ut

3+22u

2t2

+19u3t+14u

4)s2

+(t+u)3(65t

4

+ 8ut3 − 18u

2t2

+ 8u3t + 65u

4)s + 44(t + u)

4(t2

+ ut + u2)2)

H(3, y)H(1, 1, z)(s + u)6

+ 108s2t2

(s + t)6u2(t + u)

6(2s

4

+ (4t− 2u)s3

+(6t

2 − 3u2)s2

+(4t

3 − 2u3)s+ 2

(t2

+ ut+ u2)2)

H(0, 0, y) H(1, 1, z)(s+ u)6 − 108s

2t2(s+ t)

6u2(t+ u)

6(4s

4

+ (6t− 2u)s3

+ 9(t2

+ u2)s2

+ 6(t3 − u3

)s + 4

(t2

+ u t + u2)2)

H(0, 3, y)H(1, 1, z)(s + u)6

+ 216s2t2(s + t)

6u3

(t + u)6(2s

3

− 3us2

+ 4u2s + 6t

(t2 − ut + u

2))

H(0, 1, z)H(1, 2, y)(s + u)6 − 216s

2t2(s + t)

6u3(t + u)

6(6s

3 − 6u s2

+ 6u2s + t

(2t

2 − 3ut

=+4u2))H(1, 0, z)H(1, 2, y) (s+u)

6+36s

2t2(s+t)

6u2(t+u)

2(2(11t

4+32ut

3+42u

2t2

+27u3t+9u

4)s4

+(44t

5+115ut

4+95u

2t3

+9u3t2−11 u

4t+4u

5)s3

+6(t+u)2(11t

4+19ut

3+11u

2t2

+3 u4)s2

+(t+u)3(44t

4+8ut

3−9u2t2

+21u4)s+22 (t+u)

4(t2

+ut

+u2)2)

H(1, z)H(2, 0, y)(s+u)6− 108s

2t2(s+ t)

6u2(t+u)

6(2s

4− 4(t−u)s3

+ 6(2t

2+u

2)s2

+ 4u3s+ 2t

4+ 2u

4+ 2tu

3+ 3t

2u2

+ 2t3u)H(0, 0, z)H(2, 0, y) (s+ u)

6 − 108s2t2(s+ t)

6u2(t+ u)

6(4s

4+ 2(5t+ 2u)s

3+ 3

(t2

+ 2u2)s2

+ 2(7t

3+ 2u

3)s+ 4t

4+ 4u

4

+ 4t u3

+ 6t2u2

+ 4t3u)H(0, 1, z)H(2, 0, y)(s+u)

6 − 108s2t2(s+ t)

6u2(t+u)

6(4s

4+ 6ts

3+ 9(t2

+ 2u2)s2

+(6t

3+ 4 u

3)s+ 4t

4

+4u4

+6tu3

+9t2u2

+6t3u)H(1, 0, z)H(2, 0, y) (s+u)

6+3s

2t2(s+ t)

6u2(t+u)

2((

363t4

+492ut3

+504u2t2

+492u3t+363u

4)s4

+2(363t

5+479ut

4−58u2t3−58u

3t2

+479u4t+363u

5)s3

+9(t+u)2(121t

4−10ut3−134u

2t2−10u

3t+121u

4)s2

+6(t+u)3(121t

4

+ 35ut3

+ 12u2t2

+ 35u3t + 121u

4)s + 363(t + u)

4(t2

+ ut + u2)2)

H(2, 2, y)(s + u)6

+ 36s2t2(s + t)

6u2(t + u)

2(2(9t

4

+ 27u t3

+ 42u2t2

+ 32u3t + 11u

4)s4

+(4t

5 − 11ut4

+ 9u2t3

+ 95 u3t2

+ 115u4t + 44u

5)s3

+ 6(t + u)2(3t

4+ 11u

2t2

+ 19u3t + 11u

4)s2

+ (t + u)3(21t

4 − 9u2t2

+ 8u3t + 44u

4)s + 22(t + u)

4(t2

+ ut + u2)2)

H(0, z)H(2, 2, y)(s + u)6

+ 108 s2t2(s+ t)

6u2(t+ u)

6(2s

4 − 2(t− 2u)s3 − 3

(t2 − 2 u

2)s2 − 2

(t3 − 2u

3)s+ 2

(t2

+ u t+ u2)2)

H(0, 0, z)H(2, 2, y)(s+ u)6

– 26 –

= + 432s2t2(s + t)

6u2

(t + u)6(s4

+ 3(t2

+ u2)s2 −

(t3

+ u3)s +

(t2

+ ut + u2)2)

H(0, 1, z)H(2, 2, y)(s + u)6

− 108s2t2

(s+ t)6u2(t+ u)

6(4s

4 − 2(t+ 2u)s3

+ 3(5t

2+ 8u

2)s2

+ 2(t3 − 2u

3)s+ 4

(t2

+ ut+ u2)2)

H(1, 0, z) H(2, 2, y)(s+ u)6

+ 324s2t2(s + t)

6u2(t + u)

6(2s

4+ 2(t + u)s

3+ 3

(t2

+ u2)s2

+ 2(t3

+ u3)s + 2

(t2

+ u t + u2)2)

H(0, 1, z)H(2, 3, y)(s + u)6

=− 108s2t2(s + t)

6u2

(t + u)6(2s

4+ 2(t + u)s

3+ 3

(t2

+ u2)s2

+ 2(t3

+ u3)s + 2

(t2

+ ut + u2)2)

H(1, 0, z)H(2, 3, y) (s + u)6

− 18s2t2(s + t)

6u2(t + u)

3(2u(12t

2+ 15ut + 7 u

2)s4 − 12

(t4 − 2u

2t2 − 2u

3t− u4

)s3 − 3(t + u)

2(5t

3 − 31ut2 − 17u

2t

− 5u3)s2 − 6(t + u)

3(t3 − ut2 − u2

t− u3)s− (t + u)

3(3t

4 − 18ut3 − 3u

2t2

+ 4u3t + 8 u

4))H(1, z)H(3, 0, y)(s + u)

6

− 108s2t2(s + t)

6u2(t + u)

6(2s

4+ 2(t + u)s

3+ 3

(t2

+ u2)s2

+ 2(t3

+ u3)s + 2

(t2

+ ut + u2)2)

H(0, 1, z)H(3, 0, y)(s + u)6

− 108s2t2

(s + t)6u2(t + u)

6(2s

4+ 10(t + u)s

3 − 3(t2

+ u2)s2

+ 6(t3

+ u3)s + 2

(t2

+ ut + u2)2)

H(1, 0, z)H(3, 0, y) (s + u)6

− 216s2t2(s + t)

6u2(t + u)

6(2s

4+ 2ts

3+ 9t

2s2

+ 2(t2

+ ut + u2)2)

H(1, 1, z)H(3, 0, y)(s + u)6

=− 18s2t2

(s + t)6u2(t + u)

3(2t(7t

2+ 15ut + 12u

2)s4

+ 12(t4

+ 2ut3

+ 2u2t2 − u4

)s3

+ 3(t + u)2(5t

3+ 17ut

2+ 31 u

2t

− 5u3)s2

+ 6(t + u)3(t3

+ ut2

+ u2t− u3

)s− (t + u)

3(8t

4+ 4ut

3 − 3u2t2 − 18u

3t + 3u

4))H(0, z)H(3, 2, y) (s + u)

6

− 36s2t2(s + t)

6u2(t + u)

2(2(20t

4+ 59ut

3+ 84u

2t2

+ 59u3t + 20u

4)s4

+ 8(6t

5+ 13ut

4+ 13u

2t3

+ 13u3t2

+ 13u4t + 6u

5)s3

+ 6(t + u)2(14t

4+ 19ut

3+ 22u

2t2

+ 19 u3t + 14u

4)s2

+ (t + u)3(65t

4+ 8ut

3 − 18u2t2

+ 8u3t + 65 u

4)s + 44(t + u)

4(t2

+ ut

+ u2)2)

H(1, z)H(3, 2, y) (s+ u)6

+ 216s2t2(s+ t)

6u2(t+ u)

6(2s

4+ 2ts

3+ 9t

2s2

+ 2(t2

+ ut+ u2)2)

H(0, 1, z)H(3, 2, y)(s+ u)6

− 216s2t2

(s+ t)6u2(t+ u)

6(2s

4+ 4(t+ 2u)s

3 − 3(t2 − u2

)s2

+ 2(t3

+ 3u3)s+ 2

(t2

+ ut+ u2)2)

H(1, 0, z) H(3, 2, y)(s+ u)6

+ 18s2t2(s + t)

6u2(t + u)

2((

58t4

+ 340u t3

+ 540u2t2

+ 340u3t + 58u

4)s4

+ 2(21t

5+ 265ut

4+ 658u

2t3

+ 658u3t2

+ 265u4t

+ 21u5)s3

+ 6(t+ u)2(5t

4+ 86u t

3+ 138u

2t2

+ 86u3t+ 5u

4)s2

+ 2(t+ u)3(t4

+ 97ut3

+ 96 u2t2

+ 97u3t+ u

4)s+ 3(t+ u)

4(t4

+ 30ut3

+ 36u2t2

+ 30u3t+u

4))H(1, z)H(3, 3, y)(s+u)

6+ 216s

2t2(s+ t)

6u2(t+u)

6(4s

4+ (6t+ 4u)s

3+ 3(t2

+ 2u2)s2

+ 4(2 t

3

+ u3)s+ 4

(t2

+ ut+ u2)2)

H(0, 1, z)H(3, 3, y) (s+ u)6 − 216s

3t2(s+ t)

6u3(t+ u)

6(2s

2 − 3us+ 4u2)H(1, 0, z)H(3, 3, y)(s+ u)

6

+ 216s2t2(s + t)

6u2(t + u)

6(4s

4+ 2 (t + u)s

3+ 9

(t2

+ u2)s2

+ 4(t2

+ ut + u2)2)

H(1, 1, z)H(3, 3, y)(s + u)6

= + 216s2t2(s+ t)

6u2(t+ u)

6(s4

+ 2(t+ u) s3

+ 3(t2

+ u2)s2

+ 2(t3

+ u3)s+ t

4+ u

4+ 6t

2u2 − 2 t

3u)H(0, y)H(0, 0, 1, z)(s+ u)

6

+ 216s2t2(s+ t)

6u3(t+ u)

6(2s

3 − 3us2

+ 4u2s+ 6t

(t2 − ut+ u

2))H(1, y) H(0, 0, 1, z)(s+ u)

6+ 108s

2t2(s+ t)

6u2(t+ u)

6(6s

4

+2(4t+u) s3

+15u2s2

+2(6t

3−u3)s+6

(t2

+u t+u2)2)

H(2, y)H(0, 0, 1, z)(s+u)6

+432s2t2(s+ t)

6u2

(t+u)6(2s

4+2(t+u)s

3

+ 3(t2

+ u2)s2

+ 2(t3

+ u3)s+ 2

(t2

+ ut+ u2)2)

H(3, y)H(0, 0, 1, z) (s+ u)6 − 36s

2t2(s+ t)

2u2(t+ u)

6(22s

8+ 3(44t+ 7u) s

7

+(374t

2+ 63ut+ 18u

2)s6

+(660t

3+ 54ut

2+ 36u

2t+ 4 u

3)s5

+(792t

4+ 2ut

3+ 84u

2t2 − 11u

3t+ 18u

4)s4

+ t(660t

4+ 41ut

3

+ 246u2t2

+ 9u3t+ 54u

4)s3

+ t2(374 t

4+ 147ut

3+ 360u

2t2

+ 95u3t+ 84u

4)s2

+ t3(132t

4+ 140u t

3+ 246u

2t2

+ 115u3t+ 64u

4)s

+ 22t4(t2

+ u t + u2)2)

H(0, 0, 2, y)(s + u)6

+ 216s2t2(s + t)

6u2(t + u)

6(s4

+ 2ts3

+ 3(t2

+ 2u2)s2

+ 2(t3 − u3

)s + t

4+ u

4

− 2tu3

+ 6t2u2)H(0, z)H(0, 0, 2, y)(s + u)

6+ 108s

2t2

(s + t)6u2(t + u)

6(2s

4+ (4t− 2u)s

3+(6t

2 − 3u2)s2

+(4t

3 − 2u3)s

+ 2(t2

+ ut+ u2)2)

H(1, z) H(0, 0, 2, y)(s+ u)6 − 108s

2t2(s+ t)

6u2(t+ u)

6(4s

4+ 2(4t+ u) s

3+ 3(4t

2+ 5u

2)s2

+(8t

3 − 2u3)s

+ 4(t4 − u t3 + 6u

2t2 − u3

t + u4))H(1, z)H(0, 0, 3, y)(s + u)

6+ 108s

2t2

(s + t)6u2(t + u)

6(2s

4+ 2(2t + u)s

3+ 3

(2t

2+ u

2)s2

+ 2(2t

3+ u

3)s + 2t

4+ 2u

4+ 2tu

3+ 3t

2u2

+ 2t3u)H(0, z) H(0, 1, 0, y)(s + u)

6 − 108s2t2(s + t)

6u2(t + u)

6(2s

4+ 2(2t + u) s

3

+ 3(2t

2+ u

2)s2

+ 2(2t

3+ u

3)s+ 2t

4+ 2u

4+ 2t u

3+ 3t

2u2

+ 2t3u)H(1, z)H(0, 1, 0, y)(s+ u)

6+ 108s

2t2(s+ t)

6u2(t+ u)

6(2s

4

= + (4t− 6u)s3

+(6t

2+ 9u

2)s2

+(4 t

3 − 2u3)s + 2

(t4

+ u4))H(0, y)H(0, 1, 0, z) (s + u)

6 − 216s2t2(s + t)

6u3(t + u)

6(6s

3

− 6us2

+ 6u2s + t

(2t

2 − 3ut + 4u2))H(1, y)H(0, 1, 0, z)(s + u)

6 − 108s2t2

(s + t)6u2(t + u)

6(2s

4 − 2(2t + 5u)s3

+ 3(4t

2

+ 5u2)s2 − 10u

3s+ 2

(t2

+ ut+ u2)2)

H(2, y)H(0, 1, 0, z) (s+ u)6

+ 216s3t2(s+ t)

6u2(t+ u)

6(4(t+ u)s

2 − 3(t2

+ u2)s+ 2

(t3

+u3))H(3, y)H(0, 1, 0, z) (s+u)

6−36s2t2(s+ t)

6u2(t+u)

2(2(11t

4+32ut

3+42u

2t2

+27u3t+9u

4)s4

+(44t

5+115ut

4+95u

2t3

+ 9u3t2 − 11 u

4t+ 4u

5)s3

+ 6(t+ u)2(11t

4+ 19ut

3+ 11u

2t2

+ 3 u4)s2

+ (t+ u)3(44t

4+ 8ut

3 − 9u2t2

+ 21u4)s+ 22 (t+ u)

4(t2

+ ut + u2)2)

H(0, 1, 1, z)(s + u)6 − 108s

2t2

(s + t)6u2(t + u)

6(2s

4+ (4t− 2u)s

3+(6t

2 − 3u2)s2

+(4t

3 − 2u3)s + 2

(t2

+ ut

+u2)2)

H(0, y) H(0, 1, 1, z)(s+u)6

+ 216s2t2(s+ t)

6u2(t+u)

6(2s

4+ 2ts

3+ 9t

2s2

+ 2(t2

+ut+u2)2)

H(3, y)H(0, 1, 1, z)(s+u)6

– 27 –

=− 36s2t2

(s+ t)2u2(t+u)

6(22s

8+ 3(44t+ 7u)s

7+(374t

2+ 63ut+ 18 u

2)s6

+(660t

3+ 54ut

2+ 36u

2t+ 4u

3)s5

+(792 t

4+ 2ut

3

+ 84u2t2 − 11u

3t+ 18u

4)s4

+ t(660t

4+ 41u t

3+ 246u

2t2

+ 9u3t+ 54u

4)s3

+ t2(374t

4+ 147ut

3+ 360 u

2t2

+ 95u3t+ 84u

4)s2

+ t3(132t

4+ 140ut

3+ 246u

2t2

+ 115u3t+ 64u

4)s+ 22t

4(t2

+ ut+ u2)2)

H(0, 2, 0, y)(s+ u)6

+ 108s2t2(s+ t)

6u2(t+ u)

6(2s

4

+ 12us3

+ 8 u3s + 2t

4+ 2u

4+ 2tu

3+ 3t

2u2

+ 2t3u)H(0, z)H(0, 2, 0, y) (s + u)

6+ 108s

2t2(s + t)

6u2(t + u)

6(2s

4+ (4t− 2u)s

3

+(6 t

2 − 3u2)s2

+(4t

3 − 2u3)s + 2

(t2

+ u t + u2)2)

H(1, z)H(0, 2, 0, y)(s + u)6

+ 36s2t2(s + t)

6u2

(t + u)2(2(11t

4

+ 32ut3

+ 42u2t2

+ 27u3t + 9u

4)s4

+(44t

5+ 115ut

4+ 95u

2t3

+ 9u3t2 − 11u

4t + 4u

5)s3

+ 6 (t + u)2(11t

4+ 19ut

3

+ 11u2t2

+ 3u4)s2

+ (t + u)3(44 t

4+ 8ut

3 − 9u2t2

+ 21u4)s + 22(t + u)

4(t2

+ u t + u2)2)

H(0, 2, 2, y)(s + u)6

+ 108s2t2(s + t)

6u2(t + u)

6(2s

4+ 2ts

3+ 3

(t2

+ 4u2)s2

+ 2(t3 − 2u

3)s + 2

(t2

+ ut + u2)2)

H(0, z)H(0, 2, 2, y)(s + u)6

=−216s2t2

(s+t)6u2(t+u)

6(s4

+2(t−u)s3

+3(t2

+u2)s2

+2(t3−2u

3)s+t

4+u

4−4tu3

+9t2u2−4t

3u)H(1, z) H(0, 2, 3, y)(s+u)

6

− 216s2t2(s + t)

6u2(t + u)

6(2s

4+ 2(t + u)s

3+ 3

(t2

+ u2)s2

+ 2(t3

+ u3)s + 2

(t2

+ u t + u2)2)

H(1, z)H(0, 3, 0, y)(s + u)6

+ 108s2t2(s+ t)

6u2

(t+ u)6(2s

4+ 2(t+ 3u)s

3+ 3

(t2 − u2

)s2

+ 2(t3

+ 5 u3)s+ 2

(t2

+ ut+ u2)2)

H(0, z)H(0, 3, 2, y) (s+ u)6

− 108s2t2(s + t)

6u2(t + u)

6(4s

4+ (6t− 2u)s

3+ 9

(t2

+ u2)s2

+ 6(t3 − u3

)s + 4

(t2

+ u t + u2)2)

H(1, z)H(0, 3, 2, y)(s + u)6

−108s3t2(s+ t)

6u2

(t+u)6(2(t+u)s

2+3(t2−3u

2)s+2

(t3

+3 u3))H(1, z)H(0, 3, 3, y)(s+u)

6+36s

2t2(s+ t)

2u2(t+u)

6(44s

8

+ (264t + 65u)s7

+(748t

2+ 203ut + 84u

2)s6

+ 3(440t

3+ 67ut

2+ 94u

2t + 16u

3)s5

+(1584t

4+ 43u t

3+ 444u

2t2

+ 104u3t

+ 40u4)s4

+ t(1320t

4+ 43ut

3+ 492 u

2t2

+ 104u3t + 118u

4)s3

+ t2(748t

4+ 201ut

3+ 444u

2t2

+ 104u3t + 168u

4)s2

+ t3(264t

4+ 203ut

3+ 282u

2t2

+ 104 u3t + 118u

4)s + t

4(44t

4+ 65ut

3+ 84u

2t2

+ 48u3t + 40 u

4))H(1, 0, 0, y)(s + u)

6

= + 216s2t2(s + t)

6u2(t + u)

6(2 s

4+ 4ts

3+(6t

2+ 9u

2)s2

+ 2(2t

3+ u

3)s + 2

(t4

+ u4))H(0, z)H(1, 0, 0, y)(s + u)

6

− 216s2t2(s + t)

6u2(t + u)

6(2s

4+ 4ts

3+ 6t

2s2

+ 4t3s + 2t

4+ 2u

4+ 2tu

3+ 9t

2u2)H(1, z)H(1, 0, 0, y)(s + u)

6

+ 108s2t2(s + t)

6u2(t + u)

6(2 s

4+ 4(t + u)s

3+ 6

(t2

+ u2)s2

+ 4(t3

+ u3)s + 2t

4+ 2 u

4 − 2tu3 − 3t

2u2

− 2t3u)H(0, y)H(1, 0, 0, z)(s + u)

6 − 108s2t2

(s + t)6u2(t + u)

6(2s

4 − 4(t− u)s3

+ 6(2t

2+ u

2)s2

+ 4 u3s + 2t

4+ 2u

4

+ 2tu3

+ 3t2u2

+ 2t3u)H(2, y)H(1, 0, 0, z) (s + u)

6 − 108s2t2(s + t)

6u2(t + u)

6(2s

4+ 4ts

3+ 6t

2s2

+ 4t3s + 2t

4+ 2u

4

− 2tu3

+ 9t2u2 − 6t

3u)H(0, y)H(1, 0, 1, z)(s + u)

6+ 216 s

2t2(s + t)

6u3(t + u)

6(2s

3 − 3us2

+ 4u2s + 6t

(t2 − u t

+ u2))H(1, y)H(1, 0, 1, z)(s + u)

6 − 216s2t2(s + t)

6u2

(t + u)6(2(t + 2u)s

3 − 3t2s2

+(4t

3+ 6u

3)s− tu

(2 t

2+ 3ut

+ 2u2))H(2, y)H(1, 0, 1, z)(s+u)

6+ 216s

2t2(s+ t)

6u2(t+u)

6(2s

4+ 2ts

3+ 9t

2s2

+ 2(t2

+u t+u2)2)

H(3, y)H(1, 0, 1, z)(s+u)6

=− 18s2t2(s + t)

3u2

(t + u)6(8s

7+ (28t− 6u)s

6+ 3

(11t

2 − 8ut− 5u2)s5 −

(7t

3+ 42ut

2+ 81u

2t + 12u

3)s4 − 2

(28t

4+ 18u t

3

+ 105u2t2

+ 12u3t + 7u

4)s3 − 6t

(8t

4+ ut

3+ 37u

2t2

+ 4 u3t + 5u

4)s2 − 3

(3t

6 − 4ut5

+ 21u2t4

+ 8u4t2)s + 3 t

4(t3

+ 2ut2

+ 5u2t + 4u

3))H(1, 0, 2, y)(s + u)

6+ 108s

2t2(s + t)

6u2(t + u)

6(2s

4+ (4t + 6u)s

3+(6t

2 − 3u2)s2

+ 2(2t

3+ 5u

3)s + 2t

4

+ 2u4

+ 10tu3 − 3t

2u2

+ 6t3u)H(0, z)H(1, 0, 2, y)(s + u)

6 − 216s2t2(s + t)

6u3(t + u)

6(2 s

3 − 3us2

+ 4u2s + 6t

(t2 − ut

+u2))H(1, z)H(1, 0, 3, y) (s+u)

6 − 18s2t2(s+ t)

2u2(t+u)

6(3s

8+ 2(51t+u)s

7+(486 t

2+ 200ut+ 30u

2)s6

+ 6(179t

3+ 130ut

2

+ 96u2t + 7 u

3)s5

+ 2(687t

4+ 677ut

3+ 945u

2t2

+ 265u3t + 29u

4)s4

+ 2t(537t

4+ 677ut

3+ 1344u

2t2

+ 658u3t + 170u

4)s3

+ 2 t2(243t

4+ 390ut

3+ 945u

2t2

+ 658u3t + 270u

4)s2

+ 2t3(51t

4+ 100ut

3+ 288u

2t2

+ 265u3t + 170u

4)s + t

4(3 t

4+ 2ut

3

+ 30u2t2

+ 42u3t + 58u

4))H(1, 1, 0, y)(s + u)

6+ 216 s

3t2(s + t)

6u3(t + u)

6(4s

2 − 3us + 2u2)H(0, z)H(1, 1, 0, y) (s + u)

6

=− 216s2t3(s + t)

6u3(t + u)

6(4t

2 − 3ut + 2u2)H(1, z)H(1, 1, 0, y)(s + u)

6 − 216s2t2(s + t)

6u2(t + u)

6(s4

+ 2(t− u) s3

+ 3(t2

+ 2u2)s2

+ 2t3s +

(t2

+ ut + u2)2)

H(0, y)H(1, 1, 0, z)(s + u)6 − 216s

2t2(s + t)

6u3(t + u)

6(6s

3 − 6u s2

+ 6u2s + t

(2t

2 − 3ut

+ 4u2))H(1, y)H(1, 1, 0, z) (s+ u)

6 − 108s2t2(s+ t)

6u2(t+ u)

6(8s

4+ 4(2t+ u)s

3+ 12

(t2

+ 3u2)s2

+ 4(2t

3+ u

3)s+ 8t

4+ 8u

4

+ 14t u3

+ 21t2u2

+ 14t3u)H(2, y)H(1, 1, 0, z)(s + u)

6 − 216s2t2(s + t)

6u2(t + u)

6(2s

4+ 4(t + 2u)s

3 − 3(t2 − u2

)s2

+ 2(t3

+ 3u3)s+ 2

(t2

+ ut+ u2)2)

H(3, y) H(1, 1, 0, z)(s+ u)6 − 18s

2t2(s+ t)

3u2(t+ u)

6(8s

7+ (28t− 6u) s

6+ 3(11t

2 − 8ut− 5u2)s5

−(7t

3+ 42ut

2+ 81u

2t+ 12 u

3)s4− 2

(28t

4+ 18ut

3+ 105u

2t2

+ 12u3t+ 7u

4)s3− 6t

(8t

4+ut

3+ 37u

2t2

+ 4u3t+ 5u

4)s2− 3

(3 t

6

− 4ut5

+ 21u2t4

+ 8u4t2)s + 3t

4(t3

+ 2ut2

+ 5u2t + 4 u

3))H(1, 2, 0, y)(s + u)

6+ 108s

2t2(s + t)

6u2(t + u)

6(2 s

4+ (4t− 6u)s

3

+(6t

2+ 9u

2)s2

+(4t

3 − 2u3)s+ 2 t

4+ 2u

4+ 2tu

3+ 3t

2u2

+ 2t3u)H(0, z)H(1, 2, 0, y)(s+ u)

6+ 216s

2t2(s+ t)

6u3(t+ u)

6(2s

3

– 28 –

=− 3us2

+ 4u2s+ 6t

(t2 − u t+ u

2))H(1, z)H(1, 2, 3, y)(s+ u)

6 − 36s2t2(s+ t)

2u2(t+ u)

6(22s

8+ 3(44t+ 7u)s

7+(374t

2+ 63ut

+ 18u2)s6

+(660t

3+ 54ut

2+ 36u

2t + 4u

3)s5

+(792t

4+ 2u t

3+ 84u

2t2 − 11u

3t + 18u

4)s4

+ t(660t

4+ 41ut

3+ 246u

2t2

+ 9u3t + 54u

4)s3

+ t2(374t

4+ 147ut

3+ 360u

2t2

+ 95u3t + 84u

4)s2

+ t3(132t

4+ 140ut

3+ 246u

2t2

+ 115u3t + 64 u

4)s

+ 22t4(t2

+ ut + u2)2)

H(2, 0, 0, y)(s + u)6 − 108 s

2t2(s + t)

6u2(t + u)

6(2s

4+ 4(t− u)s

3+ 6

(t2

+ 2u2)s2

+ 4t3s + 2t

4

+ 2u4

+ 2tu3

+ 3t2u2

+ 2t3u)H(0, z)H(2, 0, 0, y) (s + u)

6+ 108s

2t2(s + t)

6u2(t + u)

6(2s

4+ (4t− 2u)s

3+(6 t

2 − 3u2)s2

+(4t

3 − 2u3)s + 2

(t2

+ u t + u2)2)

H(1, z)H(2, 0, 0, y)(s + u)6

+ 36s2t2(s + t)

6u2

(t + u)2(2(11t

4+ 32ut

3+ 42u

2t2

+ 27u3t

+ 9u4)s4

+(44t

5+ 115ut

4+ 95u

2t3

+ 9u3t2 − 11u

4t + 4u

5)s3

+ 6 (t + u)2(11t

4+ 19ut

3+ 11u

2t2

+ 3u4)s2

+ (t + u)3(44 t

4

+ 8ut3 − 9u

2t2

+ 21u4)s + 22(t + u)

4(t2

+ u t + u2)2)

H(2, 0, 2, y)(s + u)6 − 108s

2t2(s + t)

6u2(t + u)

6(2s

4+ 2(t + 4u)s

3

+ 3t2s2

+ 2(t3

+ 6u3)s + 2

(t4

+ u4))H(0, z)H(2, 0, 2, y)(s + u)

6 − 216s2t2(s + t)

6u2(t + u)

6(s4

+ (4t− 2u)s3

+ 3u2s2

+(6t

3 − 4u3)s +

(t2

+ ut + u2)2)

H(1, z)H(2, 0, 3, y)(s + u)6 − 108s

2t2

(s + t)6u2(t + u)

6(2s

4+ 2(2t + 5u)s

3+(6t

2

− 3u2)s2

+(4t

3+ 6u

3)s + 2t

4+ 2u

4+ 2tu

3+ 3t

2u2

+ 2t3u)H(0, z)H(2, 1, 0, y)(s + u)

6 − 216s2t2(s + t)

6u2(t + u)

6(2s

4

+ 2(2 t + u)s3

+ 3(2t

2+ u

2)s2

+ 2(2t

3+ u

3)s + 2t

4+ 2 u

4+ 2tu

3+ 3t

2u2

+ 2t3u)H(1, z)H(2, 1, 0, y)(s + u)

6

= + 36s2t2

(s + t)6u2(t + u)

2(2(11t

4+ 32ut

3+ 42u

2t2

+ 27u3t + 9 u

4)s4

+(44t

5+ 115ut

4+ 95u

2t3

+ 9u3t2 − 11u

4t

+ 4 u5)s3

+ 6(t + u)2(11t

4+ 19ut

3+ 11u

2t2

+ 3u4)s2

+ (t + u)3(44t

4+ 8ut

3 − 9u2t2

+ 21u4)s + 22(t + u)

4(t2

+ ut

+u2)2)

H(2, 2, 0, y)(s+u)6−216s

2t2(s+t)

6u2

(t+u)6(s4−2(t+u)s

3+6(t2

+u2)s2

+(t2

+u t+u2)2)

H(0, z)H(2, 2, 0, y)(s+u)6

+ 432s2t2(s + t)

6u2

(t + u)6(s4

+ 3(t2

+ u2)s2 −

(t3

+ u3)s +

(t2

+ ut + u2)2)

H(1, z)H(2, 2, 3, y)(s + u)6

− 108s2t2

(s + t)6u2(t + u)

6(2s

4+ 2(t + u)s

3+ 3

(t2

+ u2)s2

+ 2(t3

+ u3)s + 2

(t2

+ ut + u2)2)

H(1, z)H(2, 3, 0, y) (s + u)6

− 108s2t2(s + t)

6u2(t + u)

6(2s

4+ 2(t + u)s

3+ 3

(t2

+ u2)s2

+ 2(t3

+ u3)s + 2

(t2

+ u t + u2)2)

H(0, z)H(2, 3, 2, y)(s + u)6

+ 432s2t2(s + t)

6u2

(t + u)6(2s

4+ 2(t + u)s

3+ 3

(t2

+ u2)s2

+ 2(t3

+ u3)s + 2

(t2

+ ut + u2)2)

H(1, z)H(2, 3, 3, y) (s + u)6

− 18s2t2(s + t)

6u2(t + u)

3(2u(12t

2+ 15ut + 7 u

2)s4 − 12

(t4 − 2u

2t2 − 2u

3t− u4

)s3 − 3(t + u)

2(5t

3 − 31ut2 − 17u

2t

− 5u3)s2 − 6(t + u)

3(t3 − ut2 − u2

t− u3)s− (t + u)

3(3t

4 − 18ut3 − 3u

2t2

+ 4u3t + 8 u

4))H(3, 0, 2, y)(s + u)

6

=− 108s2t2(s + t)

6u2(t + u)

6(2 s

4+ 2(t− u)s

3+ 3

(t2

+ 3u2)s2

+ 2(t3 − 3u

3)s + 2

(t2

+ ut + u2)2)

H(0, z)H(3, 0, 2, y)(s + u)6

− 216s2t2

(s+ t)6u2(t+ u)

6(2s

4+ 2ts

3+ 9t

2s2

+ 2(t2

+ u t+ u2)2)

H(1, z)H(3, 0, 2, y)(s+ u)6 − 216s

3t2(s+ t)

6u3

(t+ u)6(2s

2

− 3us + 4u2)H(1, z)H(3, 0, 3, y)(s + u)

6 − 18s2t2

(s + t)6u2(t + u)

3(2u(12t

2+ 15ut + 7u

2)s4 − 12

(t4 − 2u

2t2 − 2u

3t

− u4)s3 − 3(t + u)

2(5t

3 − 31ut2 − 17 u

2t− 5u

3)s2 − 6(t + u)

3(t3 − ut2 − u2

t− u3)s− (t + u)

3(3t

4 − 18ut3 − 3u

2t2

+ 4u3t + 8u

4))H(3, 2, 0, y) (s + u)

6 − 108s2t2(s + t)

6u2(t + u)

6(2s

4+ 10(t + u)s

3 − 3(t2

+ u2)s2

+ 6(t3

+ u3)s + 2

(t2

+ u t

+u2)2)

H(0, z)H(3, 2, 0, y)(s+u)6−216s

2t2(s+ t)

6u2

(t+u)6(2s

4+2ts

3+9t

2s2

+2(t2

+ut+u2)2)

H(1, z)H(3, 2, 0, y)(s+u)6

− 36s2t2(s + t)

6u2(t + u)

2(2(20 t

4+ 59ut

3+ 84u

2t2

+ 59u3t + 20u

4)s4

+ 8(6t

5+ 13ut

4+ 13 u

2t3

+ 13u3t2

+ 13u4t + 6u

5)s3

+ 6(t + u)2(14t

4+ 19u t

3+ 22u

2t2

+ 19u3t + 14u

4)s2

+ (t + u)3(65t

4+ 8ut

3 − 18 u2t2

+ 8u3t + 65u

4)s + 44(t + u)

4(t2

+ ut

+ u2)2)

H(3, 2, 2, y)(s + u)6 − 216s

2t2(s + t)

6u2(t + u)

6(2s

4+ 2us

3+ 9u

2s2

+ 2(t2

+ ut + u2)2)

H(0, z)H(3, 2, 2, y)(s + u)6

=+216s2t2(s+ t)

6u2(t+u)

6(4s

4+2(t+u)s

3+9(t2

+u2)s2

+4(t2

+ut+u2)2)

H(1, z)H(3, 2, 3, y)(s+u)6−216s

3t3

(s+ t)6(2s

2

−3ts+4t2)u2(t+u)

6H(1, z)H(3, 3, 0, y) (s+u)

6+18s

2t2(s+t)

6u2(t+u)

2((

58t4

+340ut3

+540u2t2

+340u3t+58u

4)s4

+2(21t

5

+ 265ut4

+ 658u2t3

+ 658u3t2

+ 265u4t+ 21u

5)s3

+ 6(t+ u)2(5t

4+ 86ut

3+ 138u

2t2

+ 86u3t+ 5u

4)s2

+ 2(t+ u)3(t4

+ 97ut3

+ 96u2t2

+ 97u3t+ u

4)s+ 3(t+ u)

4(t4

+ 30ut3

+ 36u2t2

+ 30u3t+ u

4))H(3, 3, 2, y)(s+ u)

6 − 216s3t2(s+ t)

6u3(t+ u)

6(2s

2

− 3us + 4u2)H(0, z)H(3, 3, 2, y)(s + u)

6+ 216s

2t2(s + t)

6u2(t + u)

6(4s

4+ 2(t + u)s

3+ 9

(t2

+ u2)s2

+ 4(t2

+ u t

+ u2)2)

H(1, z)H(3, 3, 2, y)(s + u)6

+ 216s2t2(s + t)

6u2

(t + u)6(4s

4+ 6(t + u)s

3+ 3

(t2

+ u2)s2

+ 8(t3

+ u3)s + 4

(t2

+ ut

+ u2)2)

H(1, z)H(3, 3, 3, y) (s + u)6 − 324s

2t2(s + t)

6u3(t + u)

6(2s

3+ 3us

2+ 2u

2s− 4t

(t2 − ut + u

2))H(0, 0, 0, 1, z)(s + u)

6

– 29 –

= + 432s2t2(s + t)

6u2

(t + u)6(s4

+ (2t− u)s3

+ 3(t2

+ u2)s2

+ 2t3s + t

4+ u

4+ 3 t

2u2 − t3u

)H(0, 0, 1, 0, y)(s + u)

6

+ 432s2t2(s+ t)

6u3(t+u)

6(3s

3+ 2u

2s− 2t

3 − 3tu2)H(0, 0, 1, 0, z)(s+u)

6+ 108s

2t2

(s+ t)6u2(t+u)

6(2s

4+ (4t− 2u)s

3+(6t

2

−3u2)s2

+(4t

3−2u3)s+2

(t2

+ut+u2)2)

H(0, 0, 1, 1, z)(s+u)6

+108s2t2(s+ t)

6u2(t+u)

6(2s

4+(4t−2u) s

3+(6t

2−3u2)s2

+(4t

3 − 2u3)s+ 2

(t2

+u t+u2)2)

H(0, 0, 2, 2, y)(s+u)6 − 108s

2t2(s+ t)

6u2(t+u)

6(4s

4+ 2(4t+u)s

3+ 3(4t

2+ 5u

2)s2

+(8t

3

−2 u3)s+4

(t4−ut3 +6u

2t2−u3

t+u4))

H(0, 0, 3, 2, y)(s+u)6

+108s2t2(s+t)

6u2(t+u)

6(2s

4+4(t−u) s

3+6(t2−u2

)s2

+4(t3

−u3)s+ 2t

4+ 2u

4+ 18t u

3− 3t2u2

+ 18t3u)H(0, 1, 0, 1, z)(s+u)

6− 108s2t2(s+ t)

6u2

(t+u)6(2s

4+ 2(2t+u)s

3+ 3(2t

2+u

2)s2

+ 2(2 t

3+ u

3)s+ 2t

4+ 2u

4+ 2tu

3+ 3t

2u2

+ 2t3u)H(0, 1, 0, 2, y) (s+ u)

6+ 432s

2t2(s+ t)

6u2(t+ u)

6(2s

4+ 2(2t+ u)s

3+ 3(2 t

2

+ u2)s2

+ 2(2t

3+ u

3)s+ 2t

4+ 2u

4+ 2tu

3+ 3t

2u2

+ 2t3u)H(0, 1, 1, 0, y)(s+ u)

6+ 108s

2t2(s+ t)

6u2(t+ u)

6(2s

4+ 4(t− u)s

3

+ 6(t2

+ 2u2)s2

+ 4t3s+ 2t

4+ 2u

4 − 10 tu3

+ 3t2u2 − 6t

3u)H(0, 1, 1, 0, z)(s+u)

6 − 108s2t2(s+ t)

6u2

(t+u)6(2s

4+ 2(2t+u)s

3

+ 3(2t

2+ u

2)s2

+ 2(2 t

3+ u

3)s + 2t

4+ 2u

4+ 2tu

3+ 3t

2u2

+ 2t3u)H(0, 1, 2, 0, y) (s + u)

6+ 108s

2t2(s + t)

6u2(t + u)

6(2s

4

+ (4t− 2u)s3

+(6 t

2 − 3u2)s2

+(4t

3 − 2u3)s + 2

(t2

+ u t + u2)2)

H(0, 2, 0, 2, y)(s + u)6 − 216s

2t2(s + t)

6u2(t + u)

6(s4

+ 2(t− 2u)s3

+ 3(t2

+ u2)s2

+ 2(t3 − u3

)s + t

4+ u

4+ 4tu

3+ 6t

3u)H(0, 2, 1, 0, y)(s + u)

6+ 108s

2t2(s + t)

6u2(t + u)

6(2s

4

= + (4t− 2u)s3

+(6t

2 − 3u2)s2

+(4 t

3 − 2u3)s + 2

(t2

+ ut + u2)2)

H(0, 2, 2, 0, y) (s + u)6 − 216s

2t2(s + t)

6u2(t + u)

6(s4

+2(t−u)s3

+3(t2

+u2)s2

+2(t3−2u

3)s+ t

4+u

4−4tu3

+9t2u2−4t

3u)H(0, 2, 3, 2, y)(s+u)

6−216s2t2(s+ t)

6u2(t+u)

6(2s

4

+ 2(t+u)s3

+ 3(t2

+u2)s2

+ 2(t3

+u3)s+ 2

(t2

+ut+u2)2)

H(0, 3, 0, 2, y)(s+u)6− 216s

2t2

(s+ t)6u2(t+u)

6(2s

4+ 2(t+u)s

3

+ 3(t2

+ u2)s2

+ 2(t3

+ u3)s+ 2

(t2

+ ut+ u2)2)

H(0, 3, 2, 0, y) (s+ u)6 − 108s

2t2(s+ t)

6u2(t+ u)

6(4s

4+ (6t− 2u)s

3+ 9

(t2

+ u2)s2

+ 6(t3 − u3

)s+ 4

(t2

+ u t+ u2)2)

H(0, 3, 2, 2, y)(s+ u)6 − 108s

3t2(s+ t)

6u2(t+ u)

6(2(t+ u)s

2+ 3(t2 − 3u

2)s+ 2

(t3

+3u3))

H(0, 3, 3, 2, y)(s+u)6

+108s2t2(s+t)

6u2(t+u)

6(2s

4+(4t−6u) s

3+3(2t

2+u

2)s2

+2(2t

3−5u3)s+2

(t4−2 ut

3+6u

2t2

+u4))H(1, 0, 0, 1, z)(s+u)

6−216s2t2(s+t)

6u2(t+u)

6(2s

4+4ts

3+6t

2s2

+4t3s+2t

4+2u

4+2tu

3+9t

2u2)H(1, 0, 0, 2, y)(s+u)

6

+ 216s2t2(s + t)

6u2(t + u)

6(4 s

4+ 8ts

3+ 3

(4t

2+ 3u

2)s2

+ 2(4t

3+ u

3)s + 4 t

4+ 4u

4+ 2tu

3+ 9t

2u2)H(1, 0, 1, 0, y)(s + u)

6

= + 108s2t2(s + t)

6u2(t + u)

6(2s

4+ 2(2t + 9u)s

3+(6t

2 − 3u2)s2

+ 2(2t

3+ 9u

3)s + 2

(t4 − 2ut

3 − 3u2t2 − 2u

3t

+u4))H(1, 0, 1, 0, z)(s+u)

6−216s2t2(s+t)

6u2(t+u)

6(2s

4+4ts

3+6t

2s2

+4t3s+2t

4+2u

4+2tu

3+9t

2u2)H(1, 0, 2, 0, y)(s+u)

6

− 216s2t2(s+ t)

6u3(t+u)

6(2s

3 − 3us2

+ 4 u2s+ 6t

(t2 −ut+u

2))H(1, 0, 3, 2, y)(s+u)

6+ 216s

2t2

(s+ t)6u2(t+u)

6(4s

4+ 8ts

3

+ 3(4t

2+ 3u

2)s2

+ 2(4t

3+u

3)s+ 4t

4+ 4u

4+ 2tu

3+ 9t

2u2)H(1, 1, 0, 0, y) (s+u)

6+ 108s

2t2(s+ t)

6u2(t+u)

6(2s

4+ 4(t+u)s

3

+ 6(t2

+ u2)s2

+ 4(t3

+ u3)s + 2t

4+ 2u

4 − 2tu3 − 3t

2u2 − 2t

3u)H(1, 1, 0, 0, z)(s + u)

6 − 432s2t2(s + t)

6u3(t + u)

6(2s

3

+ 3u2s− 3t

3 − 2tu2)H(1, 1, 0, 1, z)(s + u)

6 − 216s2t3

(s + t)6u3(t + u)

6(4t

2 − 3ut + 2u2)H(1, 1, 0, 2, y)(s + u)

6

+216 s2t2(s+t)

6u2(t+u)

6(4s

4+8(t+u)s

3+3(4t

2+u

2)s2

+(8t

3+6u

3)s+4t

4+4u

4+6tu

3+3t

2u2

+8t3u)H(1, 1, 1, 0, y)(s+u)

6

+ 324s2t2(s+ t)

6u3(t+u)

6(4s

3− 4us2

+ 4 u2s− t

(2t

2+ 3ut+ 2u

2))H(1, 1, 1, 0, z)(s+u)

6− 216s2t3(s+ t)

6u3(t+u)

6(4t

2− 3ut

+2u2)H(1, 1, 2, 0, y) (s+u)

6−216s2t2(s+t)

6u2(t+u)

6(2s

4+4ts

3+6t

2s2

+4t3s+2t

4+2u

4+2tu

3+9t

2u2)H(1, 2, 0, 0, y)(s+u)

6

=− 216s3t2

(s + t)6u3(t + u)

6(4s

2 − 3us + 2u2)H(1, 2, 1, 0, y)(s + u)

6+ 216 s

2t2(s + t)

6u3(t + u)

6(2s

3 − 3us2

+ 4u2s + 6t

(t2

− u t + u2))H(1, 2, 3, 2, y)(s + u)

6+ 108s

2t2(s + t)

6u2(t + u)

6(2s

4+ (4t− 2u)s

3+(6t

2 − 3u2)s2

+(4t

3 − 2 u3)s + 2

(t2

+ ut + u2)2)

H(2, 0, 0, 2, y)(s + u)6 − 216 s

2t2(s + t)

6u2(t + u)

6(s4 − 4(t + u)s

3+ 3

(3t

2+ u

2)s2 − 2

(2t

3+ u

3)s +

(t2

+ ut + u2)2)

H(2, 0, 1, 0, y)(s + u)6

+ 108s2t2(s + t)

6u2(t + u)

6(2s

4+ (4t− 2u) s

3+(6t

2 − 3u2)s2

+(4t

3 − 2u3)s + 2

(t2

+ u t + u2)2)

H(2, 0, 2, 0, y)(s + u)6 − 216s

2t2(s + t)

6u2(t + u)

6(s4

+ (4t− 2u)s3

+ 3u2s2

+(6t

3 − 4u3)s +

(t2

+ u t

+u2)2)

H(2, 0, 3, 2, y)(s+u)6− 108s

2t2(s+ t)

6u2(t+u)

6(4s

4+ (8t− 6u)s

3+ 3(4t

2+ 3u

2)s2

+(8t

3− 2 u3)s+ 4t

4+ 4u

4+ 6tu

3

+9t2u2

+6t3u)H(2, 1, 0, 0, y) (s+u)

6−216s2t2(s+t)

6u2(t+u)

6(2s

4+2(2t+u)s

3+3(2 t

2+u

2)s2

+2(2t

3+u

3)s+2t

4+2u

4+2tu

3

+3t2u2

+2t3u)H(2, 1, 0, 2, y)(s+u)

6−108s2t2(s+ t)

6u3(t+u)

6(6s

3−9us2

+2u2s+ t

(2t

2+3ut+2u

2))

H(2, 1, 1, 0, y)(s+u)6

−216s2t2(s+t)

6u2(t+u)

6(2s

4+2(2t+u) s

3+3(2t

2+u

2)s2

+2(2t

3+u

3)s+2t

4+2u

4+2t u

3+3t

2u2

+2t3u)H(2, 1, 2, 0, y)(s+u)

6

+ 108s2t2(s + t)

6u2

(t + u)6(2s

4+ (4t− 2u)s

3+(6t

2 − 3u2)s2

+(4t

3 − 2 u3)s + 2

(t2

+ ut + u2)2)

H(2, 2, 0, 0, y)(s + u)6

– 30 –

=− 108 s2t2(s + t)

6u2(t + u)

6(4s

4 − 2(2t + u)s3

+ 3(8t

2+ 5 u

2)s2

+(2u

3 − 4t3)s + 4

(t2

+ u t + u2)2)

H(2, 2, 1, 0, y)(s + u)6

+432s2t2(s+t)

6u2(t+u)

6(s4

+3(t2

+u2)s2−(t3

+u3)s+(t2

+u t+u2)2)

H(2, 2, 3, 2, y)(s+u)6−108s

2t2(s+t)

6u2(t+u)

6(2s

4

+ 2(t+u)s3

+ 3(t2

+u2)s2

+ 2(t3

+u3)s+ 2

(t2

+ut+u2)2)

H(2, 3, 0, 2, y)(s+u)6− 108s

2t2

(s+ t)6u2(t+u)

6(2s

4+ 2(t+u)s

3

+ 3(t2

+ u2)s2

+ 2(t3

+ u3)s+ 2

(t2

+ ut+ u2)2)

H(2, 3, 2, 0, y) (s+ u)6

+ 432s2t2(s+ t)

6u2(t+ u)

6(2s

4+ 2(t+ u)s

3+ 3

(t2

+ u2)s2

+ 2(t3

+ u3)s + 2

(t2

+ u t + u2)2)

H(2, 3, 3, 2, y)(s + u)6

+ 216s3t2(s + t)

6u2(t + u)

6((6t + 4u)s

2 − 3(2t

2+ u

2)s

+ 2(3 t

3+ u

3))H(3, 0, 1, 0, y)(s+ u)

6 − 216s2t2(s+ t)

6u2(t+ u)

6(2s

4+ 2ts

3+ 9t

2s2

+ 2(t2

+ ut+ u2)2)

H(3, 0, 2, 2, y)(s+ u)6

=− 216s3t2(s+ t)

6u3(t+ u)

6(2s

2 − 3us+ 4 u2)H(3, 0, 3, 2, y)(s+ u)

6 − 216s2t2(s+ t)

6u2(t+ u)

6(2 s

4+ 2ts

3+ 9t

2s2

+ 2(t2

+ ut

+ u2)2)

H(3, 2, 0, 2, y) (s + u)6 − 216s

3t2(s + t)

6u2(t + u)

6((6t + 4u)s

2 − 3(2 t

2+ u

2)s + 2

(3t

3+ u

3))H(3, 2, 1, 0, y)(s + u)

6

−216 s2t2(s+t)

6u2(t+u)

6(2s

4+2ts

3+9t

2s2

+2(t2

+u t+u2)2)

H(3, 2, 2, 0, y)(s+u)6

+216s2t2(s+t)

6u2(t+u)

6(4s

4+2(t+u)s

3

+ 9(t2

+ u2)s2

+ 4(t2

+ u t + u2)2)

H(3, 2, 3, 2, y)(s + u)6 − 216s

3t3(s + t)

6(2s

2 − 3 ts + 4t2)u2(t + u)

6H(3, 3, 0, 2, y)(s + u)

6

− 216s3t3(s+ t)

6(2s

2 − 3ts+ 4t2)u2(t+ u)

6H(3, 3, 2, 0, y)(s+ u)

6+ 216s

2t2

(s+ t)6u2(t+ u)

6(4s

4+ 2(t+ u)s

3+ 9(t2

+ u2)s2

+ 4(t2

+ ut+ u2)2)

H(3, 3, 2, 2, y)(s+ u)6

+ 216s2t2(s+ t)

6u2(t+ u)

6(4s

4+ 6(t+ u)s

3+ 3

(t2

+ u2)s2

+ 8(t3

+ u3)s+ 4

(t2

+ ut+ u2)2)

H(3, 3, 3, 2, y) (s+ u)6 − s2t2(s+ t)

3u2(t+ u)

3(7948(t+ u)

3s10

+(39359 t

4+ 155744ut

3+ 236082u

2t2

+ 155744u3t

+39359u4)s9

+(93651t

5+434331ut

4+850587u

2t3

+850587u3t2

+434331u4t+93651u

5)s8

+3(46598t

6+240304ut

5+550627u

2t4

+ 717154 u3t3

+ 550627u4t2

+ 240304u5t + 46598u

6)s7

+(139794 t

7+ 836962ut

6+ 2146599u

2t5

+ 3271156u3t4

+ 3271156u4t3

+ 2146599u5t2

+ 836962u6t+ 139794u

7)s6

+ 3(31217t

8+ 240304ut

7+ 715533 u

2t6

+ 1216094u3t5

+ 1422608u4t4

+ 1216094u5t3

+ 715533u6t2

+ 240304u7t + 31217u

8)s5

+(39359t

9+ 434331ut

8+ 1651881 u

2t7

+ 3271156u3t6

+ 4267824u4t5

+ 4267824u5t4

= + 3271156u6t3

+ 1651881u7t2

+ 434331u8t + 39359u

9)s4

+(7948 t

10+ 155744ut

9+ 850587u

2t8

+ 2151462u3t7

+ 3271156u4t6

+ 3648282 u5t5

+ 3271156u6t4

+ 2151462u7t3

+ 850587u8t2

+ 155744u9t + 7948 u

10)s3

+ 3tu(7948t

9+ 78694ut

8+ 283529u

2t7

+550627u3t6

+715533u4t5

+715533u5t4

+550627u6t3

+283529u7t2

+78694u8t+7948u

9)s2

+ t2u2(t+u)

2(23844t

6+108056ut

5

+ 194375 u2t4

+ 224106u3t3

+ 194375u4t2

+ 108056u5t + 23844u

6)s + t

3u3(t + u)

3(7948t

4+ 15515ut

3+ 23262u

2t2

+ 15515u3t

+ 7948 u4))

(s + u)3

+ 18s2t2u2((

11t6

+ 162ut5

+ 153 u2t4

+ 884u3t3

+ 255u4t2

+ 246u5t + 33u

6)s13

+(62 t

7+ 1339ut

6

+ 2160u2t5

+ 8525u3t4

+ 7390u4t3

+ 3807u5t2

+ 1728u6t + 189u

7)s12

+ 6(26t

8+ 774ut

7+ 1639u

2t6

+ 5548u3t5

+ 7678u4t4

+ 4900u5t3

+ 2621u6t2

+ 826u7t+ 84u

8)s11

+ 2(140t

9+ 4728ut

8+ 12480u

2t7

+ 37199u3t6

+ 69840u4t5

+ 60090u5t4

+ 36224u6t3

+ 17091u7t2

+ 4188u8t+ 404u

9)s10

+(534 t

10+ 13578ut

9+ 45012u

2t8

+ 119424u3t7

+ 270061u4t6

+ 311178u5t5

+ 220301u6t4

+ 125964u7t3

+ 47997u8t2

+ 9560u9t+ 839u

10)s9

+ 3(340t

11+ 5526ut

10+ 22370u

2t9

+ 55138u3t8

+ 129254u4t7

+ 190253u5t6

= + 166896u6t5

+ 109793u7t4

+ 53466u8t3

+ 15573u9t2

+ 2466u10t+ 189u

11)s8

+ 2(736t

12+ 9471u t

11+ 44292u

2t10

+ 110988u3t9

+ 235059u4t8

+ 387831u5t7

+ 413404 u6t6

+ 317445u7t5

+ 187035u8t4

+ 72214u9t3

+ 15774u10t2

+ 1827 u11t + 116u

12)s7

+ 2(708t

13+ 9054ut

12+ 47823u

2t11

+ 134712u3t10

+ 269098u4t9

+ 435561u5t8

+ 508839u6t7

+ 430834 u7t6

+ 288621u8t5

+ 141397u9t4

+ 43186u10t3

+ 7236u11t2

+ 541 u12t+ 22u

13)s6

+ 3t(285t

13+ 4132ut

12+ 24795u

2t11

+ 81510u3t10

+ 175113u4t9

+ 286188u5t8

+ 351323u6t7

+ 311558 u7t6

+ 211822u8t5

+ 112744u9t4

+ 42788u10t3

+ 10552u11t2

+ 1454 u12t + 56u

13)s5

+ t2(294t

13+ 5499ut

12+ 38730u

2t11

+ 148723u3t10

+ 362736u4t9

+ 642597u5t8

+ 864762u6t7

+ 853029 u7t6

+ 614934u8t5

+ 328490u9t4

+ 124788u10t3

+ 32430u11t2

+ 6072u12t+ 708u

13)s4

+ 2t3(22t

13+ 707u t

12+ 6399u

2t11

+ 29412u3t10

+ 82842u4t9

+ 162087u5t8

+ 239183 u6t7

+ 267073u7t6

+ 222465u8t5

+ 137118u9t4

+ 59592u10t3

+ 16485 u11t2

+ 2553u12t + 174u

13)s3

+6t4u(t+u)

2(26 t

10+335ut

9+1643u

2t8

+4383u3t7

+7465u4t6

+9430u5t5

+8350 u6t4

+5555u7t3

+2649u8t2

+809u9t+127u

10)s2

– 31 –

=+t5u2

(t+u)3(162t

8+1164ut

7+3573u

2t6

+6255u3t5

+7589u4t4

+5865 u5t3

+3192u6t2

+1112u7t+216u

8)s+t

6u3(t+u)

6(58 t

4

+ 100ut3

+ 153u2t2

+ 100u3t+ 58u

4))H(2, y)H(1, 0, z) (s+ u)

3+ st(s+ t)

2u2(t+ u)

2(1531t(t+ u)

4s13

+ 3(3029 t

6+ 15191ut

5

+ 28746u2t4

+ 30440u3t3

+ 14567u4t2

+ 3351u5t+ 120 u

6)s12

+(25433t

7+ 151345ut

6+ 347338u

2t5

+ 471508u3t4

+ 364546u4t3

+ 144937u5t2

+ 32273u6t + 1800u

7)s11

+(44445t

8+ 300713ut

7+ 814816u

2t6

+ 1300511u3t5

+ 1362455 u4t4

+ 833113u5t3

+ 303956u6t2

+ 65055u7t + 3960u

8)s10

+(53136t

9+ 409309ut

8+ 1281415u

2t7

+ 2291071u3t6

+ 2894942 u4t5

+ 2471851u5t4

+ 1320295u6t3

+ 459769u7t2

+ 87252u8t + 5040 u

9)s9

+(44445t

10+ 409309ut

9+ 1473770u

2t8

+ 2915618u3t7

+ 4102638u4t6

+ 4464012u5t5

+ 3318386u6t4

+ 1630106u7t3

+ 508285 u8t2

+ 77799u9t + 3960u

10)s8

+(25433t

11+ 300713u t

10+ 1281415u

2t9

+2915618u3t8

+4495118u4t7

+5664674u5t6

+5440250u6t5

+3552410u7t4

+1539427u8t3

+391013u9t2

+44585 u10t+1800u

11)s7

+(9087t

12+151345ut

11+814816u

2t10

+2291071u3t9

+4102638u4t8

+5664674u5t7

+6338504u6t6

+5147724u7t5

+2865079u8t4

+ 1027309u9t3

+ 196900u10t2

+ 15021 u11t + 360u

12)s6

+ t(1531t

12+ 45573ut

11+ 347338u

2t10

+ 1300511u3t9

+ 2894942u4t8

+4464012u5t7

+5440250u6t6

+5147724u7t5

+3498698u8t4

+1616591u9t3

+448090u10t2

+58725 u11t+2287u

12)s5

+t2u(6124t

11

+86238u t10

+471508u2t9

+1362455u3t8

+2471851u4t7

+3318386u5t6

+3552410u6t5

+2865079u7t4

+1616591u8t3

+581902u9t2

= + 110862 u10t+ 7726u

11)s4

+ t3u2(9186t

10+ 91320ut

9+ 364546 u

2t8

+ 833113u3t7

+ 1320295u4t6

+ 1630106u5t5

+ 1539427u6t4

+1027309u7t3

+448090u8t2

+110862u9t+11166u

10)s3

+t4u3(t+u)

2(6124t

7+31453ut

6+75907u

2t5

+120689u3t4

+142484 u4t3

+ 102628u5t2

+ 43273u6t+ 7726u

7)s2

+ t5u4(t+ u)

4(1531t

4+ 3929ut

3+ 7371u

2t2

+ 5873u3t+ 2287u

4)s+ 360t

6u6(t+ u)

4(t2

+ ut+ u2))H(0, y)(s+ u)

2+ st

2(s+ t)

2u (t+ u)

2(1531u(t+ u)

4s13

+ 3(120t

6+ 3351ut

5+ 14567u

2t4

+ 30440u3t3

+ 28746u4t2

+15191u5t+3029u

6)s12

+(1800t

7+32273ut

6+144937u

2t5

+364546u3t4

+471508u4t3

+347338u5t2

+151345u6t+25433u

7)s11

+(3960t

8+ 65055 ut

7+ 303956u

2t6

+ 833113u3t5

+ 1362455u4t4

+ 1300511u5t3

+ 814816 u6t2

+ 300713u7t + 44445u

8)s10

+(5040t

9+ 87252u t

8+ 459769u

2t7

+ 1320295u3t6

+ 2471851u4t5

+ 2894942u5t4

+ 2291071 u6t3

+ 1281415u7t2

+ 409309u8t

+ 53136u9)s9

+(3960 t

10+ 77799ut

9+ 508285u

2t8

+ 1630106u3t7

+ 3318386u4t6

+ 4464012 u5t5

+ 4102638u6t4

+ 2915618u7t3

= + 1473770u8t2

+ 409309u9t+ 44445 u

10)s8

+(1800t

11+ 44585ut

10+ 391013u

2t9

+ 1539427 u3t8

+ 3552410u4t7

+ 5440250u5t6

+ 5664674u6t5

+ 4495118u7t4

+ 2915618u8t3

+ 1281415u9t2

+ 300713u10t+ 25433u

11)s7

+(360t

12+ 15021ut

11+ 196900u

2t10

+ 1027309u3t9

+ 2865079u4t8

+ 5147724u5t7

+ 6338504u6t6

+ 5664674u7t5

+ 4102638 u8t4

+ 2291071u9t3

+ 814816u10t2

+ 151345u11t+ 9087u

12)s6

+ u(2287t

12+ 58725ut

11+ 448090u

2t10

+ 1616591u3t9

+ 3498698u4t8

+ 5147724u5t7

+ 5440250u6t6

+ 4464012u7t5

+ 2894942 u8t4

+ 1300511u9t3

+ 347338u10t2

+ 45573u11t+ 1531u

12)s5

+ tu2(7726t

11+ 110862ut

10+ 581902u

2t9

+1616591u3t8

+2865079u4t7

+3552410u5t6

+3318386u6t5

+2471851u7t4

+1362455 u8t3

+471508u9t2

+86238u10t+6124u

11)s4

+t2u3(11166t

10+110862ut

9+448090u

2t8

+1027309u3t7

+1539427u4t6

+1630106u5t5

+1320295u6t4

+833113u7t3

+364546u8t2

+ 91320u9t + 9186u

10)s3

+ t3u4(t + u)

2(7726t

7+ 43273ut

6+ 102628 u

2t5

+ 142484u3t4

+ 120689u4t3

+ 75907u5t2

+ 31453u6t

+ 6124 u7)s2

+ t4u5(t+u)

4(2287t

4+ 5873ut

3+ 7371u

2t2

+ 3929 u3t+ 1531u

4)s+ 360t

6u6(t+u)

4(t2

+ut+u2))

H(0, z)(s+u)2

=+3t2(s+t)

2u2(t+u)

(259(t+u)

5s14

+36(43 t

6+242ut

5+651u

2t4

+764u3t3

+651u4t2

+242u5t+43u

6)s13

+(4367t

7+26163ut

6

+ 84905u2t5

+ 124733u3t4

+ 124733u4t3

+ 84905u5t2

+ 26163u6t+ 4367u

7)s12

+ 4(1920t

8+ 12056 ut

7+ 43065u

2t6

+ 78684u3t5

+ 86470u4t4

+ 78684u5t3

+ 43065u6t2

+ 12056u7t+ 1920u

8)s11

+ 6(1534t

9+ 10415ut

8+ 38108 u

2t7

+ 83108u3t6

+ 101419u4t5

+ 101419u5t4

+ 83108u6t3

+ 38108u7t2

+ 10415u8t+ 1534u

9)s10

+ 12(640t

10+ 4992ut

9+ 18355 u

2t8

+ 44658u3t7

+ 62385u4t6

+ 60940u5t5

+ 62385u6t4

+ 44658u7t3

+ 18355u8t2

+ 4992u9t+ 640u

10)s9

+(4367t

11+ 41875u t

10+ 163877u

2t9

+ 417437u3t8

+ 677572u4t7

+ 645896u5t6

+ 645896 u6t5

+ 677572u7t4

+ 417437u8t3

+ 163877u9t2

+ 41875u10t + 4367 u

11)s8

+ 2(774t

12

+ 9924ut11

+ 46320u2t10

+ 124333 u3t9

+ 232260u4t8

+ 249279u5t7

+ 198284u6t6

+ 249279u7t5

+ 232260 u8t4

+ 124333u9t3

=+46320u10t2

+9924u11t+774u

12)s7

+(259t

13+5481ut

12+35278u

2t11

+110676u3t10

+240564 u4t9

+349066u5t8

+300068u6t7

+300068u7t6

+349066u8t5

+240564 u9t4

+110676u10t3

+35278u11t2

+5481u12t+259u

13)s6

+2tu(308t

12+3564ut

11+15365u

2t10

+42591u3t9

+94706u4t8

+136033u5t7

+141098u6t6

+136033u7t5

+94706u8t4

+42591u9t3

+15365u10t2

+3564u11t+308u

12)s5

+t2u2(426t

11+3380ut

10+15835u

2t9

+65921u3t8

+171209u4t7

+259557u5t6

+259557u6t5

+171209u7t4

+65921u8t3

+15835u9t2

+ 3380u10t+ 426u

11)s4 − 2t

3u3(t+ u)

2(34t

8 − 527u t7 − 6013u

2t6 − 19815u

3t5 − 26374u

4t4 − 19815u

5t3 − 6013u

6t2 − 527 u

7t

+ 34u8)s3

+ t4u4(t + u)

3(109t

6+ 2242ut

5+ 8867u

2t4

+ 13216u3t3

+ 8867u4t2

+ 2242u5t + 109u

6)s2

+ 30t5u5

(t + u)6(10t

2

+ 23ut + 10u2)s + 120t

6u6(t + u)

5(t2

+ u t + u2))H(0, y)H(0, z)(s + u)

2 − s2t(s + t)2u(t + u)

2((

360t6

+ 2287ut5

+ 7726u2t4

+ 11166u3t3

+ 7726u4t2

+ 2287 u5t+ 360u

6)s12

+ 9(200t

7+ 1669ut

6+ 6525u

2t5

+ 12318 u3t4

+ 12318u4t3

+ 6525u5t2

+ 1669u6t

+200u7)s11

+(3960t

8+44585ut

7+196900u

2t6

+448090u3t5

+581902u4t4

+448090u5t3

+196900u6t2

+44585u7t+3960u

8)s10

– 32 –

= +(5040t

9+ 77799ut

8+ 391013u

2t7

+ 1027309u3t6

+ 1616591u4t5

+ 1616591u5t4

+ 1027309u6t3

+ 391013u7t2

+ 77799u8t

+ 5040 u9)s9

+(3960t

10+ 87252ut

9+ 508285u

2t8

+ 1539427u3t7

+ 2865079u4t6

+ 3498698u5t5

+ 2865079u6t4

+ 1539427u7t3

+ 508285 u8t2

+ 87252u9t + 3960u

10)s8

+(1800t

11+ 65055u t

10+ 459769u

2t9

+ 1630106u3t8

+ 3552410u4t7

+ 5147724u5t6

+ 5147724u6t5

+ 3552410u7t4

+ 1630106u8t3

+ 459769u9t2

+ 65055 u10t + 1800u

11)s7

+(360t

12+ 32273ut

11+ 303956u

2t10

+1320295u3t9

+3318386u4t8

+5440250u5t7

+6338504u6t6

+5440250u7t5

+3318386u8t4

+1320295u9t3

+303956u10t2

+32273 u11t

+360u12)s6

+ tu(10053t

11+144937ut

10+833113 u

2t9

+2471851u3t8

+4464012u4t7

+5664674u5t6

+5664674u6t5

+4464012u7t4

+ 2471851u8t3

+ 833113u9t2

+ 144937u10t+ 10053 u

11)s5

+ tu(1531t

12+ 43701ut

11+ 364546u

2t10

+ 1362455u3t9

+ 2894942u4t8

+4102638u5t7

+4495118u6t6

+4102638u7t5

+2894942u8t4

+1362455u9t3

+364546u10t2

+43701 u11t+1531u

12)s4

+t2u2(6124t

11

+91320u t10

+471508u2t9

+1300511u3t8

+2291071u4t7

+2915618u5t6

+2915618u6t5

+2291071u7t4

+1300511u8t3

+471508u9t2

+91320 u10t+6124u

11)s3

+ t3u3(t+u)

2(9186t

8+67866u t

7+202420u

2t6

+342110u3t5

+394775u4t4

+342110u5t3

+202420u6t2

+ 67866u7t + 9186u

8)s2

+ t4u4(t + u)

3(6124t

6+ 27201u t

5+ 51370u

2t4

+ 58876u3t3

+ 51370u4t2

+ 27201u5t + 6124u

6)s

+ t5u5(t + u)

4(1531t

4+ 2963ut

3+ 4395u

2t2

+ 2963u3t + 1531 u

4))H(1, z)(s + u)

2 − s2t(s + t)2u(t + u)

2((

360 t6

+ 2287ut5

= + 7726u2t4

+ 11166u3t3

+ 7726u4t2

+ 2287u5t+ 360 u

6)s12

+ 9(200t

7+ 1669ut

6+ 6525u

2t5

+ 12318u3t4

+ 12318u4t3

+ 6525u5t2

+ 1669u6t+ 200u

7)s11

+(3960 t

8+ 44585ut

7+ 196900u

2t6

+ 448090u3t5

+ 581902u4t4

+ 448090u5t3

+ 196900u6t2

+ 44585u7t

+ 3960u8)s10

+(5040t

9+ 77799u t

8+ 391013u

2t7

+ 1027309u3t6

+ 1616591u4t5

+ 1616591u5t4

+ 1027309 u6t3

+ 391013u7t2

+ 77799u8t + 5040u

9)s9

+(3960 t

10+ 87252ut

9+ 508285u

2t8

+ 1539427u3t7

+ 2865079u4t6

+ 3498698 u5t5

+ 2865079u6t4

+ 1539427u7t3

+ 508285u8t2

+ 87252u9t + 3960 u

10)s8

+(1800t

11+ 65055ut

10+ 459769u

2t9

+ 1630106 u3t8

+ 3552410u4t7

+ 5147724u5t6

+ 5147724u6t5

+ 3552410u7t4

+ 1630106u8t3

+ 459769u9t2

+ 65055u10t + 1800u

11)s7

+(360t

12+ 32273ut

11

+ 303956u2t10

+ 1320295u3t9

+ 3318386u4t8

+ 5440250u5t7

+ 6338504u6t6

+ 5440250u7t5

+ 3318386 u8t4

+ 1320295u9t3

+ 303956u10t2

+ 32273u11t+ 360u

12)s6

+ tu(10053t

11+ 144937ut

10+ 833113u

2t9

+ 2471851u3t8

+ 4464012u4t7

+ 5664674u5t6

+ 5664674u6t5

+ 4464012u7t4

+ 2471851 u8t3

+ 833113u9t2

+ 144937u10t+ 10053u

11)s5

+ tu(1531t

12+ 43701ut

11+ 364546u

2t10

+ 1362455u3t9

+ 2894942 u4t8

+ 4102638u5t7

+ 4495118u6t6

+ 4102638u7t5

+ 2894942u8t4

+ 1362455u9t3

+ 364546u10t2

+ 43701u11t+ 1531u

12)s4

+ t2u2(6124t

11+ 91320ut

10+ 471508u

2t9

+ 1300511u3t8

+ 2291071u4t7

+ 2915618u5t6

+ 2915618u6t5

+ 2291071u7t4

+ 1300511 u8t3

+ 471508u9t2

+ 91320u10t + 6124u

11)s3

+ t3u3(t + u)

2(9186t

8+ 67866ut

7+ 202420u

2t6

+ 342110u3t5

+ 394775u4t4

+ 342110u5t3

+ 202420u6t2

+ 67866u7t+ 9186u

8)s2

+ t4u4

(t+ u)3(6124t

6+ 27201ut

5+ 51370u

2t4

+58876u3t3

+51370u4t2

+27201u5t+6124u

6)s+t

5u5(t+u)

4(1531t

4+2963u t

3+4395u

2t2

+2963u3t+1531u

4))H(2, y)(s+u)

2

=− 3s2t2

(t+u)2((

120t6

+ 300ut5

+ 109u2t4− 68u

3t3

+ 426u4t2

+ 616 u5t+ 259u

6)s14

+ 2(420t

7+ 1395ut

6+ 1339u

2t5

+ 425u3t4

+1903u4t3

+3872u5t2

+2870u6t+774u

7)s13

+(2640 t

8+11430ut

7+18489u

2t6

+14984u3t5

+19215u4t4

+37858u5t3

+40759u6t2

+ 21396u7t + 4367u

8)s12

+ 2(2460t

9+ 13545 ut

8+ 31286u

2t7

+ 39401u3t6

+ 40878u4t5

+ 57956u5t4

+ 72977u6t3

+ 56244u7t2

+23121u8t+3840u

9)s11

+2(3000 t

10+20475ut

9+62005u

2t8

+104385u3t7

+118565u4t6

+137297u5t5

+175620u6t4

+170653u7t3

+ 102876u8t2

+ 33792u9t + 4602 u

10)s10

+ 2(2460t

11+ 20475ut

10+ 77358u

2t9

+ 164395 u3t8

+ 215383u4t7

+ 230739u5t6

+ 294815u6t5

+ 356593u7t4

+ 290657 u8t3

+ 140082u9t2

+ 35847u10t + 3840u

11)s9

+(2640 t

12+ 27090ut

11+ 124010u

2t10

+ 328790u3t9

+ 519114u4t8

+ 554262 u5t7

+ 649134u6t6

+ 963078u7t5

+ 1095009u8t4

+ 756156u9t3

+ 291138 u10t2

+ 55904u11t

+ 4367u12)s8

+ 2(420t

13+ 5715u t

12+ 31286u

2t11

+ 104385u3t10

+ 215383u4t9

+ 277131u5t8

+ 300068u6t7

+ 447563u7t6

+661734u8t5

+642258u9t4

+363648 u10t3

+110242u11t2

+15265u12t+774u

13)s7

+(120 t

14+2790ut

13+18489u

2t12

+78802u3t11

+237130u4t10

+461478u5t9

+649134u6t8

+895126u7t7

+1291792u8t6

+1479900 u9t5

+1107162u10t4

+486996u11t3

+111068u12t2

=+10260u13t+259u

14)s6

+2tu(150t

13+1339ut

12+7492u

2t11

+40878u3t10

+137297u4t9

+294815u5t8

+481539u6t7

+661734 u7t6

+ 739950u8t5

+ 608514u9t4

+ 330308u10t3

+ 104819u11

t2

+ 16074u12t + 777u

13)s5

+ t2u2(109t

12+ 850u t

11+ 19215u

2t10

+ 115912u3t9

+ 351240u4t8

+ 713186u5t7

+ 1095009 u6t6

+ 1284516u7t5

+ 1107162u8t4

+ 660616u9t3

+ 249466u10t2

+ 50940u11t

+ 3885u12)s4

+ 2t3u3(− 34t

11+ 1903u t

10+ 18929u

2t9

+ 72977u3t8

+ 170653u4t7

+ 290657u5t6

+ 378078u6t5

+ 363648u7t4

+ 243498u8t3

+ 104819u9t2

+ 25470u10t + 2590 u

11)s3

+ t4u4(t + u)

2(426t

8+ 6892ut

7+ 26549u

2t6

+ 52498u3t5

+ 74207u4t4

+ 79252u5t3

+ 58427u6t2

+ 24378u7t+ 3885 u

8)s2

+ 2t5u5(t+u)

3(308t

6+ 1946ut

5+ 3936u

2t4

+ 5167 u3t3

+ 4537u4t2

+ 2799u5t

+ 777u6)s+ t

6u6(t+ u)

4(259 t

4+ 512ut

3+ 765u

2t2

+ 512u3t+ 259u

4))H(0, z)H(2, y) (s+ u)

2+ 3s

2t2(s+ t)

6u2(t+ u)

6(363s

8

+ 726(t+ 3u)s7

+ 3(363t

2+ 796ut+ 2057u

2)s6

+ 6(121t

3+ 348ut

2+ 480u

2t+ 1815u

3)s5

+(363t

4+ 958ut

3− 297u2t2

+ 1782u3t

+ 13068 u4)s4

+ 2u(246t

4 − 58ut3 − 1296u

2t2

+ 891u3t + 5445 u

4)s3

+ u2(504t

4 − 116ut3 − 297u

2t2

+ 2880u3t + 6171 u

4)s2

– 33 –

=+2u3(246t

4+479ut

3+1044u

2t2

+1194u3t+1089 u

4)s+363u

4(t2

+ut+u2)2)

H(0, 0, z)(s+u)2

+36 s2t2(s+ t)

6u2(t+u)

6(22s

8

+ 44(t+ 3u)s7

+ 2(33t

2+ 70u t+ 187u

2)s6

+(44t

3+ 246ut

2+ 147u

2t+ 660u

3)s5

+(22t

4+ 115ut

3+ 360u

2t2

+ 41u3t+ 792u

4)s4

+u(64t

4+95ut

3+246u

2t2

+2u3t+660u

4)s3

+u2(84 t

4+9ut

3+84u

2t2

+54u3t+374u

4)s2

+u3(54t

4−11u t3

+36u2t2

+63u3t

+ 132u4)s+u

4(18t

4+ 4ut

3+ 18u

2t2

+ 21u3t+ 22u

4))H(0, y)H(0, 0, z)(s+u)

2 − 36s2t2(s+ t)

6u2(t+u)

6(22s

8+ 3(7t+ 44u)s

7

+(18t

2+ 63ut + 374u

2)s6

+(4t

3+ 36ut

2+ 54u

2t + 660u

3)s5

+(18t

4 − 11u t3

+ 84u2t2

+ 2u3t + 792u

4)s4

+ u(54t

4+ 9ut

3

+246u2t2

+41u3t+660u

4)s3

+u2(84t

4+95ut

3+360u

2t2

+147 u3t+374u

4)s2

+u3(64t

4+115ut

3+246u

2t2

+140u3t+132u

4)s

+22u4(t2

+ut+u2)2)

H(2, y)H(0, 0, z) (s+u)2

+18s2t2u2(t+u)

2((

25t4

+64ut3

+78u2t2

+44u3t+11u

4)s14

+2(92t

5+278ut

4

+ 393u2t3

+ 307u3t2

+ 133 u4t+ 27u

5)s13

+(633t

6+ 2332ut

5+ 3918u

2t4

+ 3896u3t3

+ 2351u4t2

+ 816u5t+ 124u

6)s12

+ 2(684t

7

+ 2970u t6

+ 5715u2t5

+ 6827u3t4

+ 5495u4t3

+ 2871u5t2

+ 846u6t+ 96 u

7)s11

+(2094t

8+ 10548ut

7+ 21762u

2t6

+ 27160u3t5

+ 25897u4t4

+ 19800u5t3

+ 10356u6t2

+ 2820u7t + 231u

8)s10

+ 2(1200t

9+ 6984ut

8+ 15768u

2t7

+ 19041u3t6

+ 16319u4t5

= + 14613u5t4

+ 13072u6t3

+ 7593u7t2

+ 2013u8t + 105u

9)s9

+(2094t

10+ 13968ut

9+ 35988u

2t8

+ 47158u3t7

+ 37273u4t6

+ 27528u5t5

+ 31140u6t4

+ 31554u7t3

+ 17931u8t2

+ 4336u9t + 130 u

10)s8

+ 2(684t

11+ 5274ut

10+ 15768u

2t9

+ 23579u3t8

+ 22058u4t7

+ 21537u5t6

+ 26874u6t5

+ 27399u7t4

+ 18504u8t3

+ 7571u9t2

+ 1472u10t + 24u

11)s7

+(633t

12+ 5940u t

11

+ 21762u2t10

+ 38082u3t9

+ 37273u4t8

+ 43074u5t7

+ 83288u6t6

+ 111834u7t5

+ 83094u8t4

+ 33834u9t3

+ 7744u10t2

+ 1056u11t

+ 8u12)s6

+ 2t(92t

12+ 1166ut

11+ 5715u

2t10

+ 13580u3t9

+ 16319u4t8

+ 13764u5t7

+ 26874u6t6

+ 55917u7t5

+ 62742u8t4

+ 36199u9t3

+ 9748u10t2

+ 930u11t + 72 u

12)s5

+ t2(25t

12+ 556ut

11+ 3918u

2t10

+ 13654u3t9

+ 25897u4t8

+ 29226u5t7

+ 31140u6t6

+ 54798u7t5

+ 83094u8t4

+ 72398u9t3

+ 32492u10t2

+ 6012u11t + 84u

12)s4

+ 2t3u(32t

11+ 393ut

10+ 1948u

2t9

+5495u3t8

+9900u4t7

+13072 u5t6

+15777u6t5

+18504u7t4

+16917u8t3

+9748u9t2

+3006u10t+368u

11)s3

+ t4u2(t+u)

2(78t

8

+ 458ut7

+ 1357u2t6

+ 2570u3t5

+ 3859u4t4

+ 4898u5t3

+ 4276u6t2

+ 1692u7t+ 84 u

8)s2

+ 2t5u3(t+u)

3(22t

6+ 67ut

5+ 141u

2t4

+ 200u3t3

+ 320u4t2

+ 312u5t + 72u

6)s + t

6u4(t + u)

4(11t

4+ 10u t

3+ 18u

2t2

+ 16u3t + 8u

4))H(0, z)H(0, 2, y)(s + u)

2

= + 3t2

(s+ t)u2((

17t6

+ 1338ut5

+ 1209u2t4

+ 3688u3t3

+ 4269u4t2

+ 762u5t+ 293u

6)s15

+ (t+u)2(125t

5+ 9282ut

4− 1574 u2t3

+ 24402u3t2

+ 2031u4t + 1740u

5)s14

+(421t

8+ 28668 ut

7+ 79874u

2t6

+ 122578u3t5

+ 210974u4t4

+ 216624u5t3

+ 90402u6t2

+18674u7t+4873u

8)s13

+(t+u)2(853t

7+47050u t

6+99979u

2t5

+64212u3t4

+244839u4t3

+99258u5t2

+22313u6t+8520u

7)s12

+ 4(288t

10+ 12551ut

9+ 71057u

2t8

+ 139212 u3t7

+ 179702u4t6

+ 266064u5t5

+ 276429u6t4

+ 139626u7t3

+ 41347 u8t2

+ 13917u9t

+ 2547u10)s11

+ 2(t + u)2(546t

9+ 13510 ut

8+ 92097u

2t7

+ 124154u3t6

+ 79909u4t5

+ 282798u5t4

+ 136349u6t3

+ 25806u7t2

+17949u8t+4260u

9)s10

+(745t

12+5476u t

11+88790u

2t10

+380158u3t9

+559919u4t8

+624124u5t7

+1280316 u6t6

+1630684u7t5

+ 908135u8t4

+ 264280u9t3

+ 94614u10t2

+ 32670 u11t + 4873u

12)s9

+ (t + u)2(361t

11 − 5942ut10 − 13109 u

2t9

+ 45310u3t8

− 83270u4t7 − 225424u

5t6

+ 359776u6t5

+ 341850u7t4

+ 131133u8t3

+ 49098u9t2

+ 8565u10t+ 1740u

11)s8

+(113t

14 − 5422ut13

− 49927u2t12 − 155092u

3t11 − 318038 u

4t10 − 778482u

5t9 − 1327656u

6t8 − 974758u

7t7 − 19040u

8t6

+ 432306u9t5

+ 380872u10t4

= + 185882u11t3

+ 39939u12t2

+ 2122 u13t + 293u

14)s7

+ t(t + u)2(17t

12 − 2466ut11 − 25660 u

2t10 − 88158u

3t9 − 136236u

4t8

−237708u5t7−370210u

6t6−209898 u

7t5−117978u

8t4−9304u

9t3

+43600u10t2

+14262u11t+49 u

12)s6− t2u

(424t

13+9046ut

12

+ 64296u2t11

+ 209881u3t10

+ 368916u4t9

+ 405336u5t8

+ 306108u6t7

+ 185900 u7t6

+ 201510u8t5

+ 255266u9t4

+ 158896u10t3

+ 31479u11t2 − 5494u

12t− 2252u

13)s5 − t3u2

(t+ u)2(1038 t

10+ 11826ut

9+ 41953u

2t8

+ 50370u3t7 − 10747u

4t6 − 92766u

5t5

− 113853u6t4 − 35658u

7t3

+ 15137u8t2

+ 11676u9t + 2344 u

10)s4 − t4u3

(t + u)3(1108t

8+ 5303ut

7+ 2515u

2t6 − 23685u

3t5

− 48783u4t4− 46581u

5t3− 17785u

6t2− 2753u

7t− 67 u

8)s3− t5u4

(t+u)4(133t

6− 1574ut5− 8533u

2t4− 14102 u

3t3− 10237u

4t2

− 2876u5t− 167u

6)s2

+ 30t6u5(t + u)

6(10t

3+ 37ut

2+ 37u

2t + 14u

3)s + 120t

7u6(t + u)

6(t2

+ ut + u2))H(1, 0, z)(s + u)

2

= + 18s2t2(s+ t)

2u2((

11t6

+ 162ut5

+ 129u2t4

+ 796u3t3

+ 129u4t2

+ 162u5t+ 11u

6)s12

+ 6(11t

7+ 193ut

6+ 349u

2t5

+ 1047u3t4

+ 1027u4t3

+ 313u5t2

+ 173u6t + 7u

7)s11

+(187 t

8+ 3280ut

7+ 8506u

2t6

+ 20204u3t5

+ 32372u4t4

+ 18608u5t3

+ 6910 u6t2

+ 2596u7t+ 73u

8)s10

+ 2(165t

9+ 2522ut

8+ 8324u

2t7

+ 17309u3t6

+ 35002u4t5

+ 33469u5t4

+ 14236u6t3

+ 6119u7t2

+ 1745u8t

+ 53u9)s9

+(396t

10+ 4920ut

9+ 19227u

2t8

+ 34792u3t7

+ 71793u4t6

+ 105726u5t5

+ 63533u6t4

+ 25164u7t3

+ 13635u8t2

+ 3190u9t + 168u

10)s8

+ 2(165t

11+ 1725u t

10+ 7356u

2t9

+ 10992u3t8

+ 12447u4t7

+ 31129u5t6

+ 30585u6t5

+ 10947u7t4

+9212u8t3

+6186u9t2

+1323u10t+109u

11)s7

+(187t

12+1872ut

11+8220u

2t10

+10632u3t9−15915u

4t8−29212u

5t7−9538u

6t6

− 13152u7t5

+ 1543u8t4

+ 19604u9t3

+ 10518u10t2

+ 2096u11t + 185u

12)s6

+ 2(33 t

13+ 372ut

12+ 1782u

2t11

+ 2908u3t10

− 8202u4t9 − 31332u

5t8 − 35999u

6t7 − 26337u

7t6 − 11010u

8t5

+ 8183u9t4

+ 10293u10

t3

+ 3681u11t2

+ 623u12t + 45u

13)s5

+(11t

14+ 182u t

13+ 1142u

2t12

+ 3266u3t11 − 2041u

4t10 − 30594u

5t9 − 56568 u

6t8 − 48084u

7t7 − 20480u

8t6

+ 13148u9t5

– 34 –

=+25835u10t4

+13918 u11t3

+3530u12t2

+452u13t+19u

14)s4

+2tu(10 t

13+115ut

12+604u

2t11

+1366u3t10−633u

4t9−5650u

5t8

− 5310u6t7

+ 1442u7t6

+ 9166u8t5

+ 12427u9t4

+ 8168u10t3

+ 2766u11t2

+ 499u12t+ 38u

13)s3

+ t2u2(t+ u)

2(24t

10+ 190ut

9

+ 841u2t8

+ 1482u3t7

+ 1601u4t6

+ 4172u5t5

+ 4881u6t4

+ 5362u7t3

+ 3151u8t2

+ 930u9t + 126u

10)s2

+ 2 t3u3(t + u)

3(10t

8

+ 70ut7

+ 248u2t6

+ 399u3t5

+ 669u4t4

+ 647u5t3

+ 545u6t2

+ 236u7t+ 48u

8)s+ t

4u4(t+ u)

6(11t

4+ 22ut

3+ 39u

2t2

+ 28u3t

+ 33u4))H(0, y) H(1, 0, z)(s+ u)

2+ 18s

2t2(s+ t)

2u2(4(2t

6+ 36ut

5+ 21u

2t4

+ 184u3t3

+ 21u4t2

+ 36u5t+ 2u

6)s12

+ 12(4t

7

+ 88u t6

+ 155u2t5

+ 501u3t4

+ 501u4t3

+ 155u5t2

+ 88u6t+ 4u

7)s11

+ 2(65t

8+ 1472ut

7+ 3872u

2t6

+ 9748u3t5

+ 16246u4t4

+ 9748u5t3

+ 3872u6t2

+ 1472u7t+ 65u

8)s10

+ 2(105 t

9+ 2168ut

8+ 7571u

2t7

+ 16917u3t6

+ 36199u4t5

+ 36199u5t4

+ 16917 u6t3

+7571u7t2

+2168u8t+105u

9)s9

+3(77t

10+1342u t

9+5977u

2t8

+12336u3t7

+27698u4t6

+41828u5t5

+27698u6t4

+12336u7t3

+ 5977u8t2

+ 1342u9t+ 77u

10)s8

+ 6(32 t

11+ 470ut

10+ 2531u

2t9

+ 5259u3t8

+ 9133u4t7

+ 18639u5t6

+ 18639u6t5

+ 9133u7t4

= + 5259u8t3

+ 2531u9t2

+ 470u10t+ 32 u

11)s7

+ 4(31t

12+ 423ut

11+ 2589u

2t10

+ 6536u3t9

+ 7785u4t8

+ 13437u5t7

+ 20822u6t6

+ 13437u7t5

+ 7785u8t4

+ 6536 u9t3

+ 2589u10t2

+ 423u11t+ 31u

12)s6

+ 6(9 t

13+ 136ut

12+ 957u

2t11

+ 3300u3t10

+ 4871u4t9

+ 4588u5t8

+ 7179u6t7

+ 7179u7t6

+ 4588u8t5

+ 4871u9t4

+ 3300u10t3

+ 957 u11t2

+ 136u12t + 9u

13)s5

+(11t

14+ 266u t

13

+2351u2t12

+10990u3t11

+25897u4t10

+32638u5t9

+37273 u6t8

+44116u7t7

+37273u8t6

+32638u9t5

+25897u10t4

+10990 u11t3

+2351u12t2

+266u13t+11u

14)s4

+2tu(22 t

13+307ut

12+1948u

2t11

+6827u3t10

+13580u4t9

+19041u5t8

+23579u6t7

+23579u7t6

+ 19041u8t5

+ 13580u9t4

+ 6827u10t3

+ 1948u11t2

+ 307u12t+ 22u

13)s3

+ 6t2u2(t+ u)

2(13t

10+ 105ut

9+ 430u

2t8

+ 940u3t7

+ 1317u4t6

+ 1682u5t5

+ 1317u6t4

+ 940u7t3

+ 430u8t2

+ 105u9t+ 13u

10)s2

+ 4 t3u3(t+ u)

3(16t

8+ 91ut

7+ 262u

2t6

+ 410u3t5

+530u4t4

+410u5t3

+262u6t2

+91u7t+16u

8)s+ t

4u4(t+u)

6(25t

4+34ut

3+54u

2t2

+34u3t+25u

4))H(0, z) H(2, 0, y)(s+u)

2

= + 18s2t2u2(6(11t

6+ 46ut

5+ 156u

2t4

+ 102u3t3

+ 156u4t2

+ 46u5t + 11u

6)s14

+ 2(270 t

7+ 1259ut

6+ 4389u

2t5

+ 4796u3t4

+5120u4t3

+3729u5t2

+1049u6t+204u

7)s13

+(2055t

8+10770ut

7+38032u

2t6

+57306u3t5

+58498u4t4

+54214u5t3

+27450u6t2

+ 7450u7t+ 1185u

8)s12

+ 2(2410t

9+ 14457ut

8+ 51810u

2t7

+ 97505u3t6

+ 109719u4t5

+ 108252u5t4

+ 77806u6t3

+ 32031u7t2

+8199u8t+1059u

9)s11

+(7744t

10+53588ut

9+198480u

2t8

+439066u3t7

+579501 u4t6

+598332u5t5

+517783u6t4

+294682u7t3

+ 105495u8t2

+ 24196 u9t + 2541u

10)s10

+ 2(4458t

11+ 35621ut

10+ 138966 u

2t9

+ 344982u3t8

+ 538700u4t7

+ 609874u5t6

+ 590760u6t5

+ 426236 u7t4

+ 200386u8t3

+ 62613u9t2

+ 12146u10t + 1050u

11)s9

+(7450t

12+ 68928ut

11+ 290076u

2t10

+ 782276u3t9

+ 1406634u4t8

+ 1787400u5t7

+ 1901521u6t6

+ 1654302u7t5

+ 999621 u8t4

+ 402156u9t3

+ 106839u10t2

+ 16578u11t

+ 1179u12)s8

+ 2(2230t

13+ 24137ut

12+ 113268u

2t11

+ 330723u3t10

+ 666867u4t9

+ 948111u5t8

+ 1082558u6t7

+ 1072690u7t6

= + 809304 u8t5

+ 421377u9t4

+ 148590u10t3

+ 32739u11t2

+ 3807u12t + 207 u

13)s7

+(1830t

14+ 23864ut

13+ 129744u

2t12

+ 419622 u3t11

+ 946629u4t10

+ 1526944u5t9

+ 1879479u6t8

+ 1986148u7t7

+ 1729402u8t6

+ 1108500u9t5

+ 506934u10t4

+ 157722u11

t3

+ 28413u12t2

+ 2220u13t + 69u

14)s6

+ 2t(232 t

14+ 3972ut

13+ 26409u

2t12

+ 97770u3t11

+ 247866u4t10

+ 463269u5t9

+ 652628u6t8

+ 749862u7t7

+ 712998u8t6

+ 514895 u9t5

+ 272466u10t4

+ 106176u11t3

+ 28022u12t2

+ 3996u13

t

+ 159u14)s5

+ t2(55t

14+ 1614ut

13+ 14748u

2t12

+ 66434u3t11

+ 190555u4t10

+ 406308u5t9

+ 671989u6t8

+ 896290u7t7

+ 978039u8t6

+ 811640u9t5

+ 480198u10t4

+ 201792 u11t3

+ 59561u12t2

+ 11310u13t + 1083u

14)s4

+ 2t3u(74t

13+ 1262ut

12

+ 7944u2t11

+ 27682u3t10

+ 67049u4t9

+ 125496u5t8

+ 189647u6t7

+ 237429u7t6

+ 234672u8t5

+ 169330u9t4

+ 85057u10t3

+ 28209u11t2

+ 5389u12t + 424u

13)s3

+ t4u2(t + u)

2(192t

10+ 1868ut

9+ 7244u

2t8

+ 17304u3t7

+ 30738u4t6

+ 40806u5t5

+ 45573u6t4

+ 36880u7t3

+ 20764u8t2

+ 7278u9t+ 1137u

10)s2

+ 2t5u3(t+u)

3(64t

8+ 420u t

7+ 1164u

2t6

+ 2189u3t5

+ 2787u4t4

+ 2772u5t3

+ 1870u6t2

+ 855u7t + 183u

8)s + t

6u4(t + u)

6(47t

4+ 64ut

3+ 117u

2t2

+ 92u3t + 83u

4))H(0, 1, 0, z)(s + u)

2

– 35 –

= + 36s2t2(s + t)

6u2(t + u)

6(22s

8+ 44(t + 3u)s

7+ 2

(33t

2+ 70ut + 187u

2)s6

+(44t

3+ 246ut

2+ 147u

2t + 660u

3)s5

+(22t

4

+ 115u t3

+ 360u2t2

+ 41u3t + 792u

4)s4

+ u(64t

4+ 95ut

3+ 246u

2t2

+ 2u3t + 660u

4)s3

+ u2(84t

4+ 9ut

3+ 84u

2t2

+ 54u3t

+ 374u4)s2

+ u3(54t

4 − 11ut3

+ 36u2t2

+ 63u3t + 132 u

4)s + u

4(18t

4+ 4ut

3+ 18u

2t2

+ 21u3t + 22 u

4))H(1, 0, 0, z)(s + u)

2

+ 36s2t2u3((

48t5 − 6u t

4+ 332u

2t3

+ 45u3t2

+ 90u4t + 11u

5)s14

+(420t

6+ 282u t

5+ 2684u

2t4

+ 2292u3t3

+ 810u4t2

+ 542u5t + 42u

6)s13

+(1386t

7+ 1149ut

6+ 7038u

2t5

+ 12044u3t4

+ 4972u4t3

+ 2592u5t2

+ 1202u6t + 73u

7)s12

+(2181t

8 − 6ut7

+ 3 u2t6

+ 15414u3t5

+ 7299u4t4 − 896u

5t3

+ 2931u6t2

+ 1368u7t + 106 u

8)s11

+(985t

9 − 9867ut8

− 44480u2t7 − 48559u

3t6 − 45186 u

4t5 − 50331u

5t4 − 19580u

6t3

+ 585u7t2

+ 1097u8t + 168u

9)s10 −

(2469t

10+ 31352ut

9

+ 135204u2t8

+ 241022u3t7

+ 253354 u4t6

+ 222072u5t5

+ 127806u6t4

+ 30846u7t3

+ 657u8t2 − 980u

9t− 218u

10)s9

−(5517t

11+ 52233ut

10+ 228083u

2t9

+ 506619u3t8

+ 645063u4t7

+ 575952u5t6

+ 368997u6t5

+ 131304u7t4

+ 16832u8t3

− 1527u9t2 − 936u

10t− 185u

11)s8 −

(5797 t

12+ 55314ut

11+ 250929u

2t10

+ 646444u3t9

+ 990366u4t8

+ 1001980u5t7

+ 717884u6t6

+ 319380u7t5

+ 58843u8t4 − 6082u

9t3 − 4017u

10t2 − 684u

11t− 90u

12)s7 −

(3849 t

13+ 40039ut

12+ 191778u

2t11

= + 546879u3t10

+ 969791u4t9

+ 1126182u5t8

+ 922078u6t7

+ 512534u7t6

+ 148569u8t5 − 1403u

9t4 − 14004u

10t3 − 3726u

11t2

−315u12t−19u

13)s6−t

(1647t

13+19818ut

12+104248u

2t11

+323862u3t10

+638973 u4t9

+819288u5t8

+723606u6t7

+455700u7t6

+180305u8t5

+24144 u9t4−13260u

10t3−8070u

11t2−1683u

12t−66u

13)s5− t2

(413t

13+6240ut

12+38435u

2t11

+133574u3t10

+291906u4t9

+405133u5t8

+357472u6t7

+200055u7t6

+58195u8t5−7313u

9t4−13779u

10t3−6238u

11t2−1920u

12t−309 u

13)s4

− t3(48t

13+ 1112ut

12+ 8730u

2t11

+ 35276 u3t10

+ 86245u4t9

+ 130602u5t8

+ 113599u6t7

+ 38248u7t6 − 30777 u

8t5 − 50450u

9t4

− 31999u10t3 − 10602u

11t2 − 1774u

12t− 114 u

13)s3 − t4u(t+u)

2(84t

10+ 898ut

9+ 3400u

2t8

+ 6309 u3t7

+ 5217u4t6 − 2505u

5t5

−8514u6t4−9343u

7t3−5743u

8t2−2007u

9t−336u

10)s2−t5u2

(t+u)3(48t

8+200u t

7+135u

2t6−571u

3t5−1726u

4t4−1854u

5t3

−1219u6t2−459u

7t−90u

8)s+t

6u4(t+u)

6(23t

3+54ut

2+46u

2t+26 u

3))H(1, 1, 0, z)(s+u)

2+9(s+t)

2u2(t+u)

(2(92 t

7+224ut

6

+ 807u2t5

+ 41u3t4

+ 227u4t3

+ 71u5t2

+ 70u6t+ 20 u

7)s15

+ 2(548t

8+ 1800ut

7+ 6507u

2t6

+ 5556u3t5

+ 2001 u4t4

+ 2149u5t3

+864u6t2

+535u7t+120u

8)s14

+(3080 t

9+12672ut

8+43909u

2t7

+68677u3t6

+39172u4t5

+27176u5t4

+19411u6t3

+8427u7t2

+ 3620u8t+ 640u

9)s13

+(5400 t

10+ 26796ut

9+ 85362u

2t8

+ 182471u3t7

+ 168303u4t6

+ 105098u5t5

+ 92562u6t4

+ 53097u7t3

+21885u8t2

+7050u9t+1000u

10)s12

+(6464t

11+38196ut

10+114563u

2t9

+283713u3t8

+385450 u4t7

+275704u5t6

+227431u6t5

=+183473u7t4

+90148u8t3

+33770u9t2

+8600u10t+1000u

11)s11

+(5400t

12+38196u t

11+123420u

2t10

+320669u3t9

+573417u4t8

+513000u5t7

+343086 u6t6

+321375u7t5

+218509u8t4

+96742u9t3

+32200u10t2

+6690 u11t+640u

12)s10

+(3080t

13+26796ut

12

+ 114563 u2t11

+ 320669u3t10

+ 641380u4t9

+ 698714u5t8

+ 386310u6t7

+ 282028u7t6

+ 279284u8t5

+ 162550u9t4

+ 65139u10t3

+ 18779 u11t2

+ 3220u12t + 240u

13)s9

+(1096t

14+ 12672u t

13+ 85362u

2t12

+ 283713u3t11

+ 573417u4t10

+ 698714u5t9

+ 392272u6t8

+ 129314u7t7

+ 178058u8t6

+ 158492u9t5

+ 72298u10t4

+ 25025u11t3

+ 6257u12t2

+ 870u13t+ 40u

14)s8

+ t(184t

14

+ 3600ut13

+ 43909u2t12

+ 182471u3t11

+ 385450u4t10

+ 513000u5t9

+ 386310u6t8

+ 129314u7t7

+ 92160u8t6

+ 110380u9t5

+ 48211u10t4

+ 11865u11t3

+ 3700u12t2

+ 994u13t + 100 u

14)s7

+ t2u(448t

13+ 13014ut

12+ 68677u

2t11

+ 168303u3t10

+275704u4t9

+343086u5t8

+282028u6t7

+178058 u7t6

+110380u8t5

+33784u9t4−4267u

10t3−3791u

11t2−474 u

12t+42u

13)s6

+ t3u2(1614t

12+ 11112ut

11+ 39172 u

2t10

+ 105098u3t9

+ 227431u4t8

+ 321375u5t7

+ 279284u6t6

+ 158492u7t5

+ 48211u8t4

− 4267u9t3 − 7188u

10t2 − 1770u

11t− 164u

12)s5

+ t4u3(82t

11+ 4002ut

10+ 27176u

2t9

+ 92562u3t8

+ 183473u4t7

+ 218509u5t6

+ 162550u6t5

+ 72298u7t4

+ 11865u8t3 − 3791u

9t2 − 1770u

10t− 204u

11)s4

+ t5u4

(t + u)2(454t

8+ 3390ut

7+ 12177u

2t6

+ 25353u3t5

+ 27265u4t4

+ 16859u5t3

+ 4156u6t2 − 146u

7t− 164u

8)s3

+ t6u5(t+ u)

3(142t

6+ 1302ut

5+ 4095u

2t4

+ 5552u3t3

+ 3527u4t2

+ 868u5t+ 42 u

6)s2

+ 10t7u6(t+u)

5(14t

3+ 37ut

2+ 37u

2t+ 10 u

3)s+ 40t

8u7(t+u)

5(t2

+ut+u2))H(1, 0, y) (s+u)

=− 3s2(s+ t)

2u2(t+ u)

2((

259t6

+ 616ut5

+ 426u2t4 − 68 u

3t3

+ 109u4t2

+ 300u5t+ 120u

6)s14

+ 2(774t

7+ 2870u t

6+ 3872u

2t5

+1903u3t4

+425u4t3

+1339u5t2

+1395u6t+420 u

7)s13

+(4367t

8+21396ut

7+40759u

2t6

+37858u3t5

+19215u4t4

+14984u5t3

+ 18489u6t2

+ 11430u7t + 2640u

8)s12

+ 2(3840t

9+ 23121ut

8+ 56244u

2t7

+ 72977u3t6

+ 57956u4t5

+ 40878u5t4

+ 39401u6t3

+31286u7t2

+13545u8t+2460u

9)s11

+2(4602t

10+33792ut

9+102876u

2t8

+170653u3t7

+175620 u4t6

+137297u5t5

+118565u6t4

+ 104385u7t3

+ 62005u8t2

+ 20475u9t + 3000u

10)s10

+ 2(3840t

11+ 35847ut

10+ 140082u

2t9

+ 290657u3t8

+ 356593u4t7

+ 294815u5t6

+ 230739u6t5

+ 215383u7t4

+ 164395u8t3

+ 77358u9t2

+ 20475u10t + 2460u

11)s9

+(4367t

12+ 55904ut

11

+ 291138u2t10

+ 756156u3t9

+ 1095009u4t8

+ 963078u5t7

+ 649134u6t6

+ 554262u7t5

+ 519114u8t4

+ 328790u9t3

+ 124010u10t2

+ 27090u11t + 2640u

12)s8

+ 2(774t

13+ 15265ut

12+ 110242u

2t11

+ 363648u3t10

+ 642258 u4t9

+ 661734u5t8

+ 447563u6t7

+300068u7t6

+277131u8t5

+215383 u9t4

+104385u10t3

+31286u11t2

+5715u12t+420u

13)s7

+(259t

14+10260ut

13+111068u

2t12

– 36 –

=+486996u3t11

+1107162u4t10

+1479900u5t9

+1291792u6t8

+895126u7t7

+649134u8t6

+461478u9t5

+237130u10t4

+78802u11t3

+ 18489 u12t2

+ 2790u13t + 120u

14)s6

+ 2tu(777t

13+ 16074 ut

12+ 104819u

2t11

+ 330308u3t10

+ 608514u4t9

+ 739950u5t8

+ 661734u6t7

+ 481539u7t6

+ 294815u8t5

+ 137297u9t4

+ 40878u10

t3

+ 7492u11t2

+ 1339u12t + 150u

13)s5

+ t2u2(3885 t

12

+ 50940ut11

+ 249466u2t10

+ 660616u3t9

+ 1107162u4t8

+ 1284516u5t7

+ 1095009u6t6

+ 713186u7t5

+ 351240u8t4

+ 115912u9t3

+ 19215u10t2

+ 850u11t + 109u

12)s4

+ 2t3u3(2590 t

11+ 25470ut

10+ 104819u

2t9

+ 243498u3t8

+ 363648u4t7

+ 378078 u5t6

+ 290657u6t5

+ 170653u7t4

+ 72977u8t3

+ 18929u9t2

+ 1903 u10t− 34u

11)s3

+ t4u4(t + u)

2(3885t

8+ 24378u t

7+ 58427u

2t6

+ 79252u3t5

+ 74207u4t4

+ 52498u5t3

+ 26549u6t2

+ 6892u7t+ 426u

8)s2

+ 2t5u5(t+u)

3(777t

6+ 2799u t

5+ 4537u

2t4

+ 5167u3t3

+3936u4t2

+1946u5t+308u

6)s+ t

6u6(t+u)

4(259t

4+512ut

3+765u

2t2

+512u3t+259 u

4))H(0, y)H(1, z)+9s

2(t+u)

2(2(20t

8

+ 50u t7

+ 21u2t6− 82u

3t5− 102u

4t4− 82u

5t3

+ 21u6t2

+ 50u7t+ 20 u

8)s16

+ 2(140t

9+ 505ut

8+ 568u

2t7− 298u

3t6− 1069u

4t5

− 1069u5t4 − 298u

6t3

+ 568u7t2

+ 505u8t + 140u

9)s15

+(880t

10+ 4370ut

9+ 8221u

2t8

+ 4262u3t7 − 6199u

4t6 − 10932u

5t5

−6199u6t4

+4262u7t3

+8221u8t2

+4370u9t+880 u

10)s14

+2(820t

11+5395ut

10+14563u

2t9

+17988 u3t8

+5650u4t7−8508u

5t6

=− 8508u6t5

+ 5650u7t4

+ 17988u8t3

+ 14563u9t2

+ 5395u10t+ 820u

11)s13

+(2000 t

12+ 16930ut

11+ 60889u

2t10

+ 115200u3t9

+112888u4t8

+52018 u5t7

+18062u6t6

+52018u7t5

+112888u8t4

+115200u9t3

+60889 u10t2

+16930u11t+2000u

12)s12

+2(820t

13

+ 8825 ut12

+ 40630u2t11

+ 106430u3t10

+ 162506u4t9

+ 145433u5t8

+ 94054u6t7

+ 94054u7t6

+ 145433u8t5

+ 162506u9t4

+ 106430u10

t3

+ 40630u11t2

+ 8825u12t + 820u

13)s11

+(880 t

14+ 12310ut

13+ 71305u

2t12

+ 252860u3t11

+ 542940u4t10

+ 672624u5t9

+ 495141u6t8

+ 346704u7t7

+ 495141u8t6

+ 672624 u9t5

+ 542940u10t4

+ 252860u11t3

+ 71305u12t2

+ 12310u13

t

+ 880u14)s10

+ 2(140t

15+ 2785ut

14+ 20491u

2t13

+ 99450u3t12

+ 294436u4t11

+ 490859u5t10

+ 448931u6t9

+ 254956u7t8

+254956u8t7

+448931u9t6

+490859u10t5

+294436 u11t4

+99450u12t3

+20491u13t2

+2785u14t+140u

15)s9

+(40t

16+1490ut

15

+14845u2t14

+102820u3t13

+419280 u4t12

+950788u5t11

+1225773u6t10

+975710u7t9

+743060u8t8

+975710u9t7

+1225773u10t6

+950788u11t5

+419280u12t4

+102820u13t3

+14845u14t2

+1490u15t+40u

16)s8

+2 tu(90t

15+1540ut

14+16932u

2t13

+96123u3t12

+ 304282 u4t11

+ 583798u5t10

+ 762212u6t9

+ 803305u7t8

+ 803305u8t7

+ 762212u9t6

+ 583798u10t5

+ 304282u11t4

+ 96123u12t3

+ 16932u13t2

+ 1540u14t + 90u

15)s7

+ t2u2(282 t

14+ 6622ut

13+ 54887u

2t12

+ 264008u3t11

+ 776536u4t10

+ 1517240u5t9

+ 2171441u6t8

+ 2431080u7t7

+ 2171441u8t6

+ 1517240u9t5

+ 776536u10t4

+ 264008u11t3

+ 54887u12t2

+ 6622u13t+ 282u

14)s6

= + 2t3u3(298t

13+ 4418u t

12+ 40731u

2t11

+ 190625u3t10

+ 505964u4t9

+ 877790u5t8

+ 1117090u6t7

+ 1117090u7t6

+ 877790u8t5

+ 505964u9t4

+ 190625 u10t3

+ 40731u11t2

+ 4418u12t + 298u

13)s5

+ t4u4(536t

12+ 16810ut

11+ 131975u

2t10

+ 463360u3t9

+ 936996u4t8

+ 1292362u5t7

+ 1406138u6t6

+ 1292362u7t5

+ 936996u8t4

+ 463360 u9t3

+ 131975u10t2

+ 16810u11t+ 536u

12)s4

+ 2t5u5(848t

11+ 13094ut

10+ 64600u

2t9

+ 162207u3t8

+ 255217u4t7

+ 298424u5t6

+ 298424u6t5

+ 255217u7t4

+ 162207u8t3

+ 64600u9t2

+ 13094u10t + 848u

11)s3

+ t6u6(t + u)

2(2062 t

8+ 13122ut

7+ 32971u

2t6

+ 48846u3t5

+ 54292u4t4

+ 48846u5t3

+ 32971u6t2

+ 13122u7t + 2062u

8)s2

+ 4t7u7(t + u)

3(158t

6+ 746ut

5+ 1500u

2t4

+ 1923u3t3

+ 1500u4t2

+ 746u5t + 158 u

6)s

+8t8u8(t+u)

4(23t

4+45ut

3+67u

2t2

+45u3t+23 u

4))H(1, z)H(3, y)+3s

2(s+t)u

2(t+u)

2((

17 t6−424ut

5−1038u2t4−1108u

3t3

−133u4t2

+300u5t+120u

6)s15

+(113t

7−2432ut6−9046u

2t5−13902u

3t4−8627u

4t3

+1042 u5t2

+2910u6t+840u

7)s14

+(361t

8

−5422ut7−30575u

2t6−64296u

3t5−66643u

4t4−21748u

5t3

+14031u6t2

+12270u7t+2640 u

8)s13

+(745t

9−5220ut8−49927u

2t7

− 141944u3t6 − 209881u

4t5 − 146102u

5t4 − 877u

6t3

+ 57146u7t2

+ 29730u8t + 4920 u

9)s12

+ 2(546t

10+ 2738ut

9 − 12316u2t8

−77546u3t7−169106u

4t6−184458u

5t5−65973u

6t4

+53495u7t3

+62003u8t2

+22935u9t+3000u

10)s11

+2(576t

11+14602u t

10

=+44395u2t9

+6575u3t8−159019u

4t7−299169u

5t6−202668u

6t5

+31945u7t4

+130735u8t3

+82071u9t2

+23475u10t+2460 u

11)s10

+(853t

12+ 50204ut

11+ 239326u

2t10

+ 380158u3t9 − 5759u

4t8 − 778482u

5t7 − 981862u

6t6 − 306108u

7t5

+ 310132u8t4

+ 327562u9t3

+ 138034u10t2

+ 32010u11t + 2640 u

12)s9

+(421t

13+ 48756ut

12+ 284228u

2t11

+ 643716 u3t10

+ 559919u4t9

− 346654u5t8 − 1327656u

6t7 − 1188026u

7t6 − 185900u

8t5

+ 356130u9t4

+ 244634u10t3

+ 72974u11t2

+ 14070 u12t + 840u

13)s8

+(125t

14+ 28668ut

13+ 194932u

2t12

+ 556848u3t11

+ 840628u4t10

+ 624124u5t9 − 174342u

6t8 − 974758u

7t7 − 907984u

8t6

−201510u9t5

+170032u10t4

+108262 u11t3

+22743u12t2

+3630u13t+120u

14)s7

+t(17 t

14+9532ut

13+79874u

2t12

+311220u3t11

+ 718808u4t10

+ 1133540u5t9

+ 1280316u6t8

+ 835978u7t7 − 19040u

8t6 − 455158 u

9t5 − 255266u

10t4 − 6292u

11t3

+ 26245u12t2

+ 3544u13t+ 420 u

14)s6

+ t2u(1338t

13+ 17115ut

12+ 122578u

2t11

+ 473242u3t10

+ 1064256u4t9

+ 1563708u5t8

+ 1630684u6t7

+ 1174609u7t6

+ 432306u8t5 − 92986u

9t4 − 158896u

10t3 − 40833 u

11t2

+ 2954u12t + 167u

13)s5

+ t3u2(1209 t

12+ 30536ut

11

+ 210974u2t10

+ 653148u3t9

+ 1105716u4t8

+ 1162604u5t7

+ 908135u6t6

+ 653214u7t5

+ 380872u8t4

+ 92158u9t3 − 31479u

10t2

− 16364u11t + 67u

12)s4

+ t4u3(3688 t

11+ 49261ut

10+ 216624u

2t9

+ 465668u3t8

+ 558504u4t7

+ 411820 u5t6

+ 264280u6t5

– 37 –

= + 237894u7t4

+ 185882u8t3

+ 72173u9t2

+ 5494 u10t− 2344u

11)s3

+ t5u4(t+ u)

2(4269t

8+ 21666u t

7+ 42801u

2t6

+ 45136u3t5

+ 32315u4t4

+ 22162u5t3

+ 17975u6t2

+ 9856u7t+ 2252u

8)s2

+ t6u5(t+u)

3(762t

6+ 3225u t

5+ 6713u

2t4

+ 8777u3t3

+ 5973u4t2

+1975u5t+49u

6)s+t

7u6(t+u)

4(293t

4+568ut

3+843u

2t2

+568u3t+293 u

4))H(0, 1, z)+18s

2t2(s+t)

2u2(t+u)

2((

11 t4

+20ut3

+24u2t2

+20u3t+11u

4)s14

+2(33t

5+91u t

4+115u

2t3

+119u3t2

+100u4t+44u

5)s13

+(187t

6+744 ut

5+1142u

2t4

+1208u3t3

+ 1245u4t2

+ 976u5t + 336u

6)s12

+ 2(165t

7+ 936ut

6+ 1782u

2t5

+ 1633u3t4

+ 1366u4t3

+ 1677 u5t2

+ 1363u6t + 406u

7)s11

+(396t

8+ 3450ut

7+ 8220u

2t6

+ 5816u3t5 − 2041u

4t4 − 1266u

5t3

+ 5406u6t2

+ 5360u7t + 1391 u

8)s10

+ 2(165t

9+ 2460ut

8

+ 7356u2t7

+ 5316u3t6 − 8202 u

4t5 − 15297u

5t4 − 5650u

6t3

+ 4428u7t2

+ 4099u8t+ 897u

9)s9

+(187t

10+ 5044ut

9+ 19227u

2t8

+ 21984u3t7 − 15915u

4t6 − 62664u

5t5 − 56568u

6t4 − 10620u

7t3

+ 14826u8t2

+ 9784u9t + 1783 u

10)s8

+ 2(33t

11+ 1640ut

10

+ 8324u2t9

+ 17396u3t8

+ 12447u4t7 − 14606u

5t6 − 35999u

6t5 − 24042u

7t4

+ 1442u8t3

+ 9648u9t2

+ 4481u10t + 668u

11)s7

+(11t

12+ 1158u t

11+ 8506u

2t10

+ 34618u3t9

+ 71793u4t8

+ 62258u5t7 − 9538u

6t6 − 52674u

7t5 − 20480u

8t4

+ 18332u9t3

+ 18756u10t2

+ 6076u11

t + 702u12)s6

+ 2u(81t

12+ 1047ut

11+ 10102u

2t10

+ 35002u3t9

+ 52863u4t8

+ 30585u5t7 − 6576u

6t6

=− 11010u7t5

+ 6574u8t4

+ 12427u9t3

+ 6297u10t2

+ 1397u11t+ 113 u

12)s5

+ u2(129t

12+ 6282ut

11+ 32372u

2t10

+ 66938 u3t9

+ 63533u4t8

+ 21894u5t7

+ 1543u6t6

+ 16366u7t5

+ 25835u8t4

+ 16336u9t3

+ 5137u10t2

+ 760u11t + 33u

12)s4

+ 2tu3(398t

11

+3081ut10

+9304u2t9

+14236u3t8

+12582u4t7

+9212 u5t6

+9802u6t5

+10293u7t4

+6959u8t3

+2766u9t2

+591u10t+48 u

11)s3

+t2u4(t+u)

2(129t

8+1620ut

7+3541u

2t6

+3536 u3t5

+3022u4t4

+2792u5t3

+1912u6t2

+746u7t+126u

8)s2

+2t3u5(t+u)

3(81t

6

+276ut5

+227u2t4

+155u3t3

+173u4t2

+112u5t+38u

6)s+ t

4u6(t+u)

4(11t

4−2ut3

+15u2t2

+14u3t+19u

4))H(0, y)H(0, 1, z)

−18s2t2u2(t+u)

2((

47t4

+116ut3

+144u2t2

+96u3t+39u

4)s16

+2(211t

5+697ut

4+1032u

2t3

+886u3t2

+487u4t+147u

5)s15

+ 3(587t

6+ 2466ut

5+ 4371u

2t4

+ 4476u3t3

+ 3059u4t2

+ 1466u5t+ 355u

6)s14

+ 2(2246t

7+ 11795ut

6+ 25344u

2t5

+ 30555u3t4

+ 24384u4t3

+ 14649u5t2

+ 6280u6t+ 1255u

7)s13

+(7761t

8+ 49924ut

7+ 132409u

2t6

+ 195056u3t5

+ 184034u4t4

+ 125820u5t3

+ 68009u6t2

+ 25468u7t + 4325u

8)s12

+ 6(1587t

9+ 12289ut

8+ 40330u

2t7

+ 74208u3t6

+ 86445u4t5

+ 69435 u5t4

+ 42172u6t3

+20076u7t2

+6418u8t+944u

9)s11

+(8447t

10+78224ut

9+319917u

2t8

+731786u3t7

+1046888 u4t6

+1017372u5t5

+727368u6t4

= + 404718u7t3

+ 167685u8t2

+ 44164 u9t + 5599u

10)s10

+ 2(2688t

11+ 30091ut

10+ 156379 u

2t9

+ 443281u3t8

+ 763361u4t7

+878974u5t6

+745371u6t5

+500624 u7t4

+259751u8t3

+91571u9t2

+19006u10t+2015u

11)s9

+3(784t

12+11080ut

11+75305u

2t10

+ 263492u3t9

+ 545731u4t8

+ 746656u5t7

+ 740518u6t6

+ 577912u7t5

+ 364335u8t4

+ 170508u9t3

+ 50345u10t2

+ 7940u11t

+ 660u12)s8

+ 2(318 t

13+ 6360ut

12+ 59340u

2t11

+ 252696u3t10

+ 631038u4t9

+ 1061526u5t8

+ 1285210u6t7

+ 1158562u7t6

+806991u8t5

+444563 u9t4

+181058u10t3

+45120u11t2

+5167u12t+295u

13)s7

+(80t

14+3066ut

13+43714u

2t12

+225298u3t11

+ 680647 u4t10

+ 1441224u5t9

+ 2222801u6t8

+ 2456276u7t7

+ 1932681u8t6

+ 1122364u9t5

+ 510799u10t4

+ 177102u11t3

+37210u12t2

+2790u13t+80u

14)s6

+6tu(58t

13+1689u t

12+11116u

2t11

+42847u3t10

+116103u4t9

+225254u5t8

+308029u6t7

+293932u7t6

+196649u8t5

+94795u9t4

+34537u10t3

+9491u11t2

+1574u12t+58u

13)s5

+t2u2(1092 t

12+11428ut

11+67756u

2t10

+ 245052u3t9

+ 575825u4t8

+ 929600 u5t7

+ 1064520u6t6

+ 875584u7t5

+ 515905u8t4

+ 213096u9t3

+ 59096 u10t2

+ 10508u11t

+ 1092u12)s4

+ 2t3u3(394 t

11+ 5820ut

10+ 29696u

2t9

+ 83756u3t8

+ 156154u4t7

+ 208169u5t6

+ 204213u6t5

+ 148024u7t4

+ 77656u8t3

+ 27425u9t2

+ 5475u10t+ 394u

11)s3

+ 6t4u4(t+u)

2(173t

8+ 987ut

7+ 2643u

2t6

+ 4684u3t5

+ 5690u4t4

+ 4568u5t3

+ 2519u6t2

+ 941u7t + 173 u

8)s2

+ 2t5u5(t + u)

3(150t

6+ 629ut

5+ 1361u

2t4

+ 1851 u3t3

+ 1353u4t2

+ 606u5t + 150u

6)s

+66t6u6(t+u)

4(t2

+ut+u2)2)

H(2, y)H(0, 1, z)−3s2(s+t)

2u2(t+u)

2((

259t6

+616ut5

+426u2t4−68u

3t3

+109u4t2

+300u5t

+ 120u6)s14

+ 2(774t

7+ 2870ut

6+ 3872u

2t5

+ 1903u3t4

+ 425u4t3

+ 1339u5t2

+ 1395u6t + 420u

7)s13

+(4367 t

8+ 21396ut

7

= + 40759u2t6

+ 37858u3t5

+ 19215u4t4

+ 14984u5t3

+ 18489u6t2

+ 11430u7t + 2640u

8)s12

+ 2(3840t

9+ 23121 ut

8+ 56244u

2t7

+ 72977u3t6

+ 57956u4t5

+ 40878u5t4

+ 39401u6t3

+ 31286u7t2

+ 13545u8t+ 2460u

9)s11

+ 2(4602 t

10+ 33792ut

9+ 102876u

2t8

+ 170653u3t7

+ 175620u4t6

+ 137297u5t5

+ 118565u6t4

+ 104385u7t3

+ 62005u8t2

+ 20475u9t + 3000 u

10)s10

+ 2(3840t

11

+ 35847ut10

+ 140082u2t9

+ 290657u3t8

+ 356593u4t7

+ 294815u5t6

+ 230739u6t5

+ 215383u7t4

+ 164395u8t3

+ 77358u9t2

+ 20475u10t + 2460u

11)s9

+(4367t

12+ 55904ut

11+ 291138u

2t10

+ 756156u3t9

+ 1095009u4t8

+ 963078u5t7

+ 649134u6t6

+ 554262u7t5

+ 519114u8t4

+ 328790u9t3

+ 124010u10t2

+ 27090u11t + 2640u

12)s8

+ 2(774t

13+ 15265ut

12+ 110242u

2t11

+ 363648u3t10

+ 642258 u4t9

+ 661734u5t8

+ 447563u6t7

+ 300068u7t6

+ 277131u8t5

+ 215383 u9t4

+ 104385u10t3

+ 31286u11t2

+ 5715u12t + 420u

13)s7

+(259t

14+ 10260ut

13+ 111068u

2t12

+ 486996u3t11

+ 1107162u4t10

+ 1479900u5t9

+ 1291792u6t8

+ 895126u7t7

+ 649134u8t6

+ 461478u9t5

+ 237130u10t4

+ 78802u11t3

+ 18489 u12t2

+ 2790u13t + 120u

14)s6

+ 2tu(777t

13

+ 16074 ut12

+ 104819u2t11

+ 330308u3t10

+ 608514u4t9

+ 739950u5t8

+ 661734u6t7

+ 481539u7t6

+ 294815u8t5

+ 137297u9t4

– 38 –

= + 40878u10

t3

+ 7492u11t2

+ 1339u12t + 150u

13)s5

+ t2u2(3885 t

12+ 50940ut

11+ 249466u

2t10

+ 660616u3t9

+ 1107162u4t8

+ 1284516u5t7

+ 1095009u6t6

+ 713186u7t5

+ 351240u8t4

+ 115912u9t3

+ 19215u10t2

+ 850u11t + 109u

12)s4

+ 2t3u3(2590 t

11

+25470ut10

+104819u2t9

+243498u3t8

+363648u4t7

+378078 u5t6

+290657u6t5

+170653u7t4

+72977u8t3

+18929u9t2

+1903 u10t

−34u11)s3

+t4u4(t+u)

2(3885t

8+24378u t

7+58427u

2t6

+79252u3t5

+74207u4t4

+52498u5t3

+26549u6t2

+6892u7t+426u

8)s2

+2t5u5(t+u)

3(777t

6+2799u t

5+4537u

2t4

+5167u3t3

+3936u4t2

+1946u5t+308u

6)s+ t

6u6(t+u)

4(259t

4+512ut

3+765u

2t2

+512u3t+259 u

4))H(0, 2, y)−18s

2t2u2(t+u)

3(2t(7t

2+15u t+12u

2)s16

+12(8t

4+24ut

3+29u

2t2

+12u3t−u4

)s15

+3(101t

5

+ 423ut4

+ 720u2t3

+ 556u3t2

+ 111 u4t− 31u

5)s14

+(598t

6+ 3066ut

5+ 7134u

2t4

+ 8992u3t3

+ 5154u4t2

+ 510u5t− 318u

6)s13

+(851t

7+ 4495u t

6+ 13290u

2t5

+ 25506u3t4

+ 26949u4t3

+ 12309u5t2

+ 688u6t− 652 u

7)s12

+ 6(158t

8+ 586ut

7+ 2628u

2t6

+ 7708u3t5

+ 11649 u4t4

+ 9092u5t3

+ 3324u6t2

+ 218u7t− 155u

8)s11

+(851 t

9 − 417ut8

+ 9564u2t7

+ 62150u3t6

+ 123813u4t5

+ 121269u5t4

+ 67982 u6t3

+ 23208u7t2

+ 2838u8t− 1002u

9)s10

+ 2(299 t

10 − 2075ut9 − 1896u

2t8

+ 23751u3t7

+ 72903u4t6

+97515u5t5

+71423u6t4

+31963u7t3

+10800u8t2

+1966u9t−409u

10)s9

+3(101t

11−1463ut10−3896u

2t9

+208u3t8

+20429u4t7

= + 58669u5t6

+ 80268u6t5

+ 55172u7t4

+ 19400u8t3

+ 4832u9t2

+ 1000u10t− 156u

11)s8

+ 2(48t

12 − 1128ut11 − 4410 u

2t10

− 17090u3t9 − 31983u

4t8

+ 6084u5t7

+ 100874u6t6

+ 143160 u7t5

+ 88338u8t4

+ 23800u9t3

+ 2622u10t2

+ 582u11t− 81 u

12)s7

+(14t

13 − 572ut12 − 3036u

2t11 − 35818u

3t10 − 106376u

4t9 − 101688u

5t8

+ 48822u6t7

+ 213630u7t6

+ 239397u8t5

+ 134809u9t4

+ 31274u10t3−36u

11t2

+ 157u12t−25 u

13)s6−6tu

(8t

12+ 37ut

11+ 3213u

2t10

+ 11984u3t9

+ 14592u4t8

+ 1987u5t7−12914u

6t6

− 20563u7t5 − 20499u

8t4 − 11612u

9t3 − 2423u

10t2

+ 147u11t + 3u

12)s5

+ t2u2(102t

11 − 5234ut10 − 25530u

2t9 − 39126u

3t8

−12408u4t7

+24648u5t6

+35505u6t5

+40505u7t4

+40476u8t3

+21240u9t2

+3629u10t−267u

11)s4

+2t3u3(−266t

10−1804u t9

− 4752u2t8 − 4830u

3t7

+ 378u4t6

+ 5301u5t5

+ 6806u6t4

+ 6178u7t3

+ 3642u8t2

+ 1119u9t + 156u

10)s3

+ 3t4u4(t + u)

2(16 t

7

− 382ut6 − 532u

2t5

+ 8u3t4

+ 467u4t3

+ 637u5t2

+ 265u6t− 71 u

7)s2 − 2t

5u5(t+u)

3(48t

5+ 151ut

4 − 84u2t3

+ 18u3t2 − 160u

4t

−15u5)s+t

6u7(t+u)

3(12t

3+3ut

2+2u

2t−11u

3))H(1, z)H(0, 3, y)−3s

2(s+ t)

2u2(t+u)

2((

259t6

+616ut5

+426u2t4−68u

3t3

+109u4t2

+300u5t+120u

6)s14

+2(774t

7+2870ut

6+3872u

2t5

+1903u3t4

+425u4t3

+1339u5t2

+1395u6t+420u

7)s13

+(4367 t

8

+ 21396ut7

+ 40759u2t6

+ 37858u3t5

+ 19215u4t4

+ 14984u5t3

+ 18489u6t2

+ 11430u7t + 2640u

8)s12

+ 2(3840t

9+ 23121 ut

8

+ 56244u2t7

+ 72977u3t6

+ 57956u4t5

+ 40878u5t4

+ 39401u6t3

+ 31286u7t2

+ 13545u8t+ 2460u

9)s11

+ 2(4602 t

10+ 33792ut

9

+ 102876u2t8

+ 170653u3t7

+ 175620u4t6

+ 137297u5t5

+ 118565u6t4

+ 104385u7t3

+ 62005u8t2

+ 20475u9t + 3000 u

10)s10

= + 2(3840t

11+ 35847ut

10+ 140082u

2t9

+ 290657u3t8

+ 356593u4t7

+ 294815u5t6

+ 230739u6t5

+ 215383u7t4

+ 164395u8t3

+ 77358u9t2

+ 20475u10t + 2460u

11)s9

+(4367t

12+ 55904ut

11+ 291138u

2t10

+ 756156u3t9

+ 1095009u4t8

+ 963078u5t7

+ 649134u6t6

+ 554262u7t5

+ 519114u8t4

+ 328790u9t3

+ 124010u10t2

+ 27090u11t + 2640u

12)s8

+ 2(774t

13+ 15265ut

12

+ 110242u2t11

+ 363648u3t10

+ 642258 u4t9

+ 661734u5t8

+ 447563u6t7

+ 300068u7t6

+ 277131u8t5

+ 215383 u9t4

+ 104385u10t3

+ 31286u11t2

+ 5715u12t + 420u

13)s7

+(259t

14+ 10260ut

13+ 111068u

2t12

+ 486996u3t11

+ 1107162u4t10

+ 1479900u5t9

+ 1291792u6t8

+ 895126u7t7

+ 649134u8t6

+ 461478u9t5

+ 237130u10t4

+ 78802u11t3

+ 18489 u12t2

+ 2790u13t + 120u

14)s6

+ 2tu(777t

13+ 16074 ut

12+ 104819u

2t11

+ 330308u3t10

+ 608514u4t9

+ 739950u5t8

+ 661734u6t7

+ 481539u7t6

+ 294815u8t5

+ 137297u9t4

+ 40878u10

t3

+ 7492u11t2

+ 1339u12t + 150u

13)s5

+ t2u2(3885 t

12+ 50940ut

11+ 249466u

2t10

+ 660616u3t9

+ 1107162u4t8

+ 1284516u5t7

+ 1095009u6t6

+ 713186u7t5

+ 351240u8t4

+ 115912u9t3

+ 19215u10t2

+ 850u11t + 109u

12)s4

+ 2t3u3(2590 t

11+ 25470ut

10+ 104819u

2t9

+ 243498u3t8

+ 363648u4t7

+ 378078 u5t6

+ 290657u6t5

+ 170653u7t4

+ 72977u8t3

= + 18929u9t2

+ 1903 u10t− 34u

11)s3

+ t4u4(t + u)

2(3885t

8+ 24378u t

7+ 58427u

2t6

+ 79252u3t5

+ 74207u4t4

+ 52498u5t3

+ 26549u6t2

+ 6892u7t + 426u

8)s2

+ 2t5u5(t + u)

3(777t

6+ 2799u t

5+ 4537u

2t4

+ 5167u3t3

+ 3936u4t2

+ 1946u5t + 308u

6)s

+ t6u6(t+ u)

4(259t

4+ 512ut

3+ 765u

2t2

+ 512u3t+ 259 u

4))H(2, 0, y)− 18s

2t2u2(t+ u)

2((

83t4

+ 224u t3

+ 312u2t2

+ 224u3t

+83u4)s16

+(646t

5+2236ut

4+3738 u

2t3

+3738u3t2

+2236u4t+646u

5)s15

+3(795t

6+3434u t

5+6735u

2t4

+8252u3t3

+6735u4t2

+3434u5t+795u

6)s14

+(5590t

7+29722ut

6+68154u

2t5

+96362u3t4

+96362u4t3

+68154u5t2

+29722u6t+5590u

7)s13

+(9297t

8

+ 59792u t7

+ 162893u2t6

+ 265856u3t5

+ 307366u4t4

+ 265856u5t3

+ 162893u6t2

+ 59792u7t+ 9297u

8)s12

+ 6(1912t

9+ 14697ut

8

+ 48146 u2t7

+ 92627u3t6

+ 123322u4t5

+ 123322u5t4

+ 92627u6t3

+ 48146u7t2

+ 14697u8t+ 1912u

9)s11

+(10571t

10+ 97460ut

9

+ 390525 u2t8

+ 895950u3t7

+ 1372200u4t6

+ 1560372u5t5

+ 1372200u6t4

+ 895950u7t3

+ 390525u8t2

+ 97460u9t+ 10571u

10)s10

+ 2(3555t

11+ 40253ut

10+ 202415u

2t9

+ 561210u3t8

+ 989305u4t7

+ 1257298u5t6

+ 1257298u6t5

+ 989305u7t4

+ 561210u8t3

+ 202415u9t2

+ 40253u10t + 3555u

11)s9

+ 3(1100t

12+ 16144u t

11+ 105097u

2t10

+ 356156u3t9

+ 736699u4t8

+ 1061804u5t7

+ 1182566u6t6

+ 1061804u7t5

+ 736699u8t4

+ 356156u9t3

+ 105097 u10t2

+ 16144u11t + 1100u

12)s8

+ 2(471t

13+ 10059u t

12

– 39 –

=+89007u2t11

+370856u3t10

+918809u4t9

+1568172u5t8

+2010976u6t7

+2010976u7t6

+1568172u8t5

+918809u9t4

+370856 u10t3

+ 89007u11t2

+ 10059u12t + 471u

13)s7

+(124 t

14+ 5166ut

13+ 68942u

2t12

+ 360694u3t11

+ 1093775u4t10

+ 2281660u5t9

+ 3515021u6t8

+ 4060864u7t7

+ 3515021u8t6

+ 2281660u9t5

+ 1093775u10t4

+ 360694u11t3

+ 68942u12t2

+ 5166u13t+ 124u

14)s6

+ 6tu(102t

13+ 2718u t

12+ 19299u

2t11

+ 75952u3t10

+ 198691u4t9

+ 370135u5t8

+ 503605u6t7

+ 503605u7t6

+ 370135u8t5

+ 198691u9t4

+ 75952u10

t3

+ 19299u11t2

+ 2718u12t + 102u

13)s5

+ t2u2(1752 t

12+ 21508ut

11+ 127396u

2t10

+ 438996u3t9

+ 986209u4t8

+ 1559032u5t7

+ 1808388u6t6

+ 1559032u7t5

+ 986209u8t4

+ 438996 u9t3

+ 127396u10t2

+ 21508u11t+ 1752u

12)s4

+ 2t3u3(834t

11+ 10755ut

10+ 52845u

2t9

+ 146657u3t8

+ 271322u4t7

+ 363015u5t6

+ 363015u6t5

+ 271322u7t4

+ 146657u8t3

+52845u9t2

+10755u10t+834u

11)s3

+6t4u4(t+u)

2(283 t

8+1733ut

7+4779u

2t6

+8360u3t5

+10092u4t4

+8360u5t3

+4779u6t2

+1733u7t+283u

8)s2

+2t5u5(t+u)

3(282t

6+1178u t

5+2417u

2t4

+3162u3t3

+2417u4t2

+1178u5t+282u

6)s+110 t

6u6(t+u)

4(t2

+ut+u2)2)

H(1, z)H(2, 3, y) + 9s2

(t+u)2(2(20t

8+ 50ut

7+ 21u

2t6 − 82u

3t5 − 102u

4t4 − 82 u

5t3

+ 21u6t2

+ 50u7t+ 20u

8)s16

+ 2(140t

9+ 505u t

8+ 568u

2t7 − 298u

3t6 − 1069u

4t5 − 1069u

5t4 − 298u

6t3

+ 568u7t2

+ 505u8t+ 140u

9)s15

+(880t

10+ 4370ut

9

=+8221u2t8

+4262u3t7−6199u

4t6−10932u

5t5−6199u

6t4

+4262u7t3

+8221 u8t2

+4370u9t+880u

10)s14

+2(820t

11+5395u t

10

+ 14563u2t9

+ 17988u3t8

+ 5650u4t7 − 8508u

5t6 − 8508u

6t5

+ 5650u7t4

+ 17988u8t3

+ 14563u9t2

+ 5395u10t + 820u

11)s13

+(2000t

12+16930ut

11+60889u

2t10

+115200u3t9

+112888u4t8

+52018u5t7

+18062u6t6

+52018u7t5

+112888u8t4

+115200u9t3

+ 60889u10t2

+ 16930u11t + 2000u

12)s12

+ 2(820t

13+ 8825ut

12+ 40630u

2t11

+ 106430u3t10

+ 162506u4t9

+ 145433u5t8

+94054u6t7

+94054u7t6

+145433u8t5

+162506u9t4

+106430u10t3

+40630u11t2

+8825u12t+820 u

13)s11

+(880t

14+12310ut

13

+ 71305u2t12

+ 252860 u3t11

+ 542940u4t10

+ 672624u5t9

+ 495141u6t8

+ 346704u7t7

+ 495141u8t6

+ 672624u9t5

+ 542940u10t4

+ 252860u11t3

+ 71305 u12t2

+ 12310u13t + 880u

14)s10

+ 2(140t

15+ 2785u t

14+ 20491u

2t13

+ 99450u3t12

+ 294436u4t11

+ 490859u5t10

+ 448931u6t9

+ 254956u7t8

+ 254956u8t7

+ 448931u9t6

+ 490859 u10t5

+ 294436u11t4

+ 99450u12t3

+ 20491u13t2

+ 2785u14

t + 140u15)s9

+(40t

16+ 1490ut

15+ 14845u

2t14

+ 102820u3t13

+ 419280u4t12

+ 950788u5t11

+ 1225773u6t10

+ 975710u7t9

+ 743060u8t8

+ 975710u9t7

+ 1225773u10t6

+ 950788u11t5

+ 419280u12t4

+ 102820u13t3

+ 14845u14t2

+ 1490u15t

+ 40u16)s8

+ 2tu(90t

15+ 1540u t

14+ 16932u

2t13

+ 96123u3t12

+ 304282u4t11

+ 583798u5t10

+ 762212u6t9

+ 803305u7t8

+ 803305u8t7

+ 762212u9t6

+ 583798 u10t5

+ 304282u11t4

+ 96123u12t3

+ 16932u13t2

+ 1540u14

t + 90u15)s7

+ t2u2(282t

14

=+6622ut13

+54887u2t12

+264008u3t11

+776536u4t10

+1517240u5t9

+2171441u6t8

+2431080u7t7

+2171441u8t6

+1517240u9t5

+ 776536u10t4

+ 264008 u11t3

+ 54887u12t2

+ 6622u13t + 282u

14)s6

+ 2t3u3(298t

13+ 4418ut

12+ 40731u

2t11

+ 190625u3t10

+ 505964u4t9

+ 877790u5t8

+ 1117090u6t7

+ 1117090u7t6

+ 877790u8t5

+ 505964u9t4

+ 190625u10t3

+ 40731u11t2

+ 4418u12t

+ 298u13)s5

+ t4u4(536t

12+ 16810ut

11+ 131975u

2t10

+ 463360u3t9

+ 936996u4t8

+ 1292362u5t7

+ 1406138u6t6

+ 1292362u7t5

+ 936996 u8t4

+ 463360u9t3

+ 131975u10t2

+ 16810u11t + 536u

12)s4

+ 2t5u5(848t

11+ 13094ut

10+ 64600u

2t9

+ 162207u3t8

+255217u4t7

+298424u5t6

+298424u6t5

+255217u7t4

+162207u8t3

+64600u9t2

+13094u10t+848u

11)s3

+ t6u6(t+u)

2(2062t

8

+ 13122ut7

+ 32971u2t6

+ 48846u3t5

+ 54292u4t4

+ 48846 u5t3

+ 32971u6t2

+ 13122u7t + 2062u

8)s2

+ 4t7u7(t + u)

3(158t

6

+746ut5

+1500u2t4

+1923u3t3

+1500u4t2

+746u5t+158 u

6)s+8t

8u8(t+u)

4(23t

4+45ut

3+67u

2t2

+45u3t+23 u

4))H(3, 2, y)

=−36s2t2u3(t+u)

2(−12t

(4t

2+7 ut+4u

2)s16−

(413t

4+1112ut

3+1066u

2t2

+344u3t−23 u

4)s15−3

(549t

5+2080ut

4+2910u

2t3

+ 1760u3t2

+ 293 u4t− 64u

5)s14 −

(3849t

6+ 19818ut

5+ 38435u

2t4

+ 35276 u3t3

+ 14007u4t2

+ 482u5t− 715u

6)s13 −

(5797t

7

+ 40039u t6

+ 104248u2t5

+ 133574u3t4

+ 86245u4t3

+ 21235u5t2 − 2834u

6t− 1572u

7)s12 − 3

(1839t

8+ 18438ut

7+ 63926u

2t6

+ 107954 u3t5

+ 97302u4t4

+ 43534u5t3

+ 4746u6t2 − 2870u

7t− 757u

8)s11 −

(2469t

9+ 52233ut

8+ 250929u

2t7

+ 546879u3t6

+ 638973u4t5

+ 405133u5t4

+ 113599u6t3− 8307u

7t2− 12530u

8t− 2258u

9)s10

+(985t

10− 31352ut9− 228083u

2t8− 646444u

3t7

− 969791u4t6− 819288u

5t5− 357472u

6t4− 38248u

7t3

+ 28876u8t2

+ 11404u9t+ 1557u

10)s9

+ 3(727t

11− 3289ut10− 45068u

2t9

−168873u3t8−330122u

4t7−375394u

5t6−241202u

6t5−66685u

7t4

+10259u8t3

+10981u9t2

+2326u10t+240u

11)s8

+(1386t

12

−6ut11−44480u

2t10−241022u

3t9−645063u

4t8−1001980u

5t7−922078u

6t6−455700u

7t5−58195u

8t4

+50450u9t3

+22836u10t2

+ 2866u11t + 202u

12)s7

+(420 t

13+ 1149ut

12+ 3u

2t11 − 48559u

3t10 − 253354u

4t9 − 575952u

5t8 − 717884u

6t7 − 512534u

7t6

−180305u8t5

+7313u9t4

+31999u10t3

+10093u11t2

+729u12t+26u

13)s6

+3t(16 t

13+94ut

12+2346u

2t11

+5138u3t10−15062u

4t9

− 74024u5t8 − 122999u

6t7 − 106460u

7t6 − 49523u

8t5 − 8048u

9t4

+ 4593u10t3

+ 3534u11t2

+ 893u12t+ 30u

13)s5

+ t2u(− 6 t

12

+ 2684ut11

+ 12044u2t10

+ 7299u3t9 − 50331u

4t8 − 127806u

5t7 − 131304u

6t6 − 58843u

7t5

+ 1403u8t4

+ 13260u9t3

+ 6238u10t2

+ 1774u11t + 336u

12)s4

+ 2t3u2(166t

11+ 1146u t

10+ 2486u

2t9 − 448u

3t8 − 9790u

4t7 − 15423u

5t6 − 8416u

6t5

+ 3041 u7t4

– 40 –

= + 7002u8t3

+ 4035u9t2

+ 960u10t+ 57u

11)s3

+ 3t4u3(t+ u)

2(15t

8+ 240ut

7+ 369u

2t6 − u3

t5 − 172u

4t4

+ 126u5t3

+ 429u6t2

+ 355u7t+ 103u

8)s2

+ t5u4(t+u)

3(90 t

6+ 272ut

5+ 116u

2t4

+ 114u3t3

+ 135u4t2

+ 117u5t+ 66u

6)s+ t

6u5(t+u)

4(11t

4− 2ut3

+ 15u2t2

+ 14u3t+ 19 u

4))H(0, 0, 1, z) + 18s

2t2(s+ t)

2u2(2(55t

6+ 282 ut

5+ 849u

2t4

+ 834u3t3

+ 876u4t2

+ 306u5t+ 62u

6)s14

+ 2(330t

7+ 2024ut

6+ 6897u

2t5

+ 10755u3t4

+ 10754u4t3

+ 8154u5t2

+ 2583u6t+ 471u

7)s13

+ 2(935t

8+ 6797ut

7+ 25584u

2t6

+ 52845u3t5

+ 63698u4t4

+ 57897u5t3

+ 34471u6t2

+ 10059u7t+ 1650 u

8)s12

+ 2(1650t

9+ 14229ut

8+ 58953u

2t7

+ 146657u3t6

+219498u4t5

+227856u5t4

+180347u6t3

+89007u7t2

+24216u8t+3555u

9)s11

+(3960t

10+40664ut

9+189546u

2t8

+542644 u3t7

+ 986209u4t6

+ 1192146u5t5

+ 1093775u6t4

+ 741712u7t3

+ 315291 u8t2

+ 80506u9t + 10571u

10)s10

+ 2(1650t

11+ 20332u t

10

+ 110712u2t9

+ 363015u3t8

+ 779516u4t7

+ 1110405u5t6

+ 1140830 u6t5

+ 918809u7t4

+ 534234u8t3

+ 202415u9t2

+ 48730u10t

+ 5736 u11)s9

+(1870t

12+ 28458ut

11+ 189546u

2t10

+ 726030 u3t9

+ 1808388u4t8

+ 3021630u5t7

+ 3515021u6t6

+ 3136344u7t5

+ 2210097u8t4

+ 1122420u9t3

+ 390525u10t2

+ 88182u11t + 9297 u

12)s8

+ 2(330t

13+ 6797ut

12+ 58953u

2t11

+ 271322 u3t10

+779516u4t9

+1510815u5t8

+2030432u6t7

+2010976u7t6

+1592706u8t5

+989305u9t4

+447975u10t3

+144438u11t2

+29896 u12t

+ 2795u13)s7

+(110t

14+ 4048ut

13+ 51168u

2t12

+ 293314u3t11

+ 986209u4t10

+ 2220810u5t9

+ 3515021u6t8

+ 4021952u7t7

= + 3547698u8t6

+ 2514596u9t5

+ 1372200u10t4

+ 555762u11t3

+ 162893u12t2

+ 29722u13t+ 2385u

14)s6

+ 2u(282t

14+ 6897ut

13

+52845u2t12

+219498u3t11

+596073u4t10

+1140830u5t9

+1568172u6t8

+1592706u7t7

+1257298u8t6

+780186u9t5

+369966u10t4

+ 132928u11t3

+ 34077 u12t2

+ 5151u13t + 323u

14)s5

+ u2(1698t

14+ 21510u t

13+ 127396u

2t12

+ 455712u3t11

+ 1093775u4t10

+ 1837618u5t9

+ 2210097u6t8

+ 1978610u7t7

+ 1372200u8t6

+ 739932u9t5

+ 307366 u10t4

+ 96362u11t3

+ 20205u12t2

+ 2236u13t

+ 83u14)s4

+ 2tu3(834t

13+ 10754ut

12+ 57897u

2t11

+ 180347u3t10

+ 370856u4t9

+ 534234u5t8

+ 561210u6t7

+ 447975u7t6

+ 277881 u8t5

+ 132928u9t4

+ 48181u10t3

+ 12378u11t2

+ 1869u12t+ 112 u

13)s3

+ t2u4(t+u)

2(1752t

10+ 12804ut

9+ 41582u

2t8

+ 82046u3t7

+ 109617u4t6

+ 103550u5t5

+ 73808u6t4

+ 37710u7t3

+ 13665u8t2

+ 3114u9t + 312u

10)s2

+ 2t3u5(t + u)

3(306t

8

+ 1665ut7

+ 4146u2t6

+ 6477u3t5

+ 6719u4t4

+ 4996u5t3

+ 2469u6t2

+ 782u7t+ 112u

8)s+ t

4u6(t+u)

6(124 t

4+ 198ut

3+ 252u

2t2

+ 148u3t + 83u

4))H(0, 1, 0, y)− 18s

2t2u2(t + u)

3(2t(7t

2+ 15ut + 12u

2)s16

+ 12(8 t

4+ 24ut

3+ 29u

2t2

+ 12u3t− u4

)s15

+ 3(101t

5+ 423u t

4+ 720u

2t3

+ 556u3t2

+ 111u4t− 31u

5)s14

+(598 t

6+ 3066ut

5+ 7134u

2t4

+ 8992u3t3

+ 5154u4t2

+ 510u5t

− 318 u6)s13

+(851t

7+ 4495ut

6+ 13290u

2t5

+ 25506u3t4

+ 26949 u4t3

+ 12309u5t2

+ 688u6t− 652u

7)s12

+ 6(158t

8+ 586u t

7

+ 2628u2t6

+ 7708u3t5

+ 11649u4t4

+ 9092u5t3

+ 3324u6t2

+ 218 u7t− 155u

8)s11

+(851t

9 − 417ut8

+ 9564u2t7

+ 62150u3t6

= + 123813u4t5

+ 121269u5t4

+ 67982u6t3

+ 23208u7t2

+ 2838u8t− 1002u

9)s10

+ 2(299t

10 − 2075ut9 − 1896u

2t8

+ 23751 u3t7

+ 72903u4t6

+ 97515u5t5

+ 71423u6t4

+ 31963u7t3

+ 10800u8t2

+ 1966u9t− 409u

10)s9

+ 3(101t

11 − 1463ut10 − 3896 u

2t9

+208u3t8

+20429u4t7

+58669u5t6

+80268u6t5

+55172u7t4

+19400u8t3

+4832u9t2

+1000u10t−156u

11)s8

+2(48t

12−1128ut11

− 4410u2t10 − 17090u

3t9 − 31983u

4t8

+ 6084u5t7

+ 100874u6t6

+ 143160u7t5

+ 88338u8t4

+ 23800u9t3

+ 2622u10t2

+ 582u11t

− 81u12)s7

+(14t

13 − 572u t12 − 3036u

2t11 − 35818u

3t10 − 106376u

4t9 − 101688u

5t8

+ 48822 u6t7

+ 213630u7t6

+ 239397u8t5

+134809u9t4

+31274u10t3−36 u

11t2

+157u12t−25u

13)s6−6tu

(8t

12+37u t

11+3213u

2t10

+11984u3t9

+14592u4t8

+1987u5t7

− 12914u6t6 − 20563u

7t5 − 20499u

8t4 − 11612u

9t3 − 2423u

10t2

+ 147u11t + 3 u

12)s5

+ t2u2(102t

11 − 5234ut10 − 25530u

2t9

− 39126 u3t8 − 12408u

4t7

+ 24648u5t6

+ 35505u6t5

+ 40505u7t4

+ 40476u8t3

+ 21240u9t2

+ 3629u10t− 267u

11)s4

+ 2t3u3(

− 266 t10 − 1804ut

9 − 4752u2t8 − 4830u

3t7

+ 378u4t6

+ 5301u5t5

+ 6806 u6t4

+ 6178u7t3

+ 3642u8t2

+ 1119u9t + 156u

10)s3

+ 3t4u4

(t + u)2(16t

7 − 382ut6 − 532u

2t5

+ 8u3t4

+ 467u4t3

+ 637u5t2

+ 265u6t− 71u

7)s2 − 2t

5u5(t + u)

3(48t

5+ 151ut

4

− 84 u2t3

+ 18u3t2 − 160u

4t− 15u

5)s + t

6u7(t + u)

3(12t

3+ 3 ut

2+ 2u

2t− 11u

3))H(0, 3, 2, y)− 18s

2t2u2(t + u)

2((

55t4

= + 148ut3

+ 192u2t2

+ 128u3t+ 47u

4)s16

+ 2(232t

5+ 807ut

4+ 1262u

2t3

+ 1126u3t2

+ 612u4t+ 173u

5)s15

+ 6(305t

6+ 1324ut

5

+ 2458u2t4

+ 2648u3t3

+ 1862u4t2

+ 872 u5t + 201u

6)s14

+ 2(2230t

7+ 11932ut

6+ 26409u

2t5

+ 33217 u3t4

+ 27682u4t3

+ 16830u5t2

+ 7005u6t+ 1347u

7)s13

+(7450t

8+ 48274ut

7+ 129744u

2t6

+ 195540u3t5

+ 190555u4t4

+ 134098u5t3

+ 72590u6t2

+ 26532u7t + 4375u

8)s12

+ 6(1486t

9+ 11488ut

8+ 37756u

2t7

+ 69937u3t6

+ 82622u4t5

+ 67718 u5t4

+ 41832u6t3

+ 19931u7t2

+ 6288u8t+ 910u

9)s11

+(7744t

10+ 71242ut

9+ 290076u

2t8

+ 661446u3t7

+ 946629 u4t6

+ 926538u5t5

+ 671989u6t4

+ 379294u7t3

+ 157923u8t2

+ 41472 u9t + 5271u

10)s10

+ 2(2410t

11+ 26794ut

10+ 138966 u

2t9

+ 391138u3t8

+ 666867u4t7

+ 763472u5t6

+652628u6t5

+448145 u7t4

+237429u8t3

+84416u9t2

+17568u10t+1903u

11)s9

+3(685t

12+9638ut

11+66160u

2t10

+229988u3t9

+ 468878u4t8

+ 632074u5t7

+ 626493u6t6

+ 499908u7t5

+ 326013u8t4

+ 156448u9t3

+ 46699u10t2

+ 7420u11t + 638u

12)s8

+ 2(270 t

13+ 5385ut

12+ 51810u

2t11

+ 219533u3t10

+ 538700u4t9

+ 893700u5t8

+ 1082558u6t7

+ 993074u7t6

+ 712998u8t5

+405820u9t4

+169330u10t3

+42843u11t2

+4984u12t+295u

13)s7

+(66t

14+2518ut

13+38032u

2t12

+195010u3t11

+579501 u4t10

– 41 –

=+1219748u5t9

+1901521u6t8

+2145380u7t7

+1729402u8t6

+1029790u9t5

+480198u10t4

+170114u11t3

+36457u12t2

+2808u13t

+83u14)s6

+6tu(46t

13+1463u t

12+9551u

2t11

+36573u3t10

+99722u4t9

+196920u5t8

+275717 u6t7

+269768u7t6

+184750u8t5

+90822u9t4

+33632u10t3

+9403 u11t2

+1592u12t+61u

13)s5

+ t2u2(936t

12+9592 ut

11+58498u

2t10

+216504u3t9

+517783u4t8

+ 852472u5t7

+ 999621u6t6

+ 842754u7t5

+ 506934u8t4

+ 212352u9t3

+ 59561u10

t2

+ 10778u11t + 1137u

12)s4

+ 2t3u3(306t

11

+ 5120u t10

+ 27107u2t9

+ 77806u3t8

+ 147341u4t7

+ 200386u5t6

+ 201078u6t5

+ 148590u7t4

+ 78861u8t3

+ 28022u9t2

+ 5655u10t

+ 424 u11)s3

+ 3t4u4(t+u)

2(312t

8+ 1862ut

7+ 5114u

2t6

+ 9264u3t5

+ 11523u4t4

+ 9432u5t3

+ 5226u6t2

+ 1942u7t+ 361 u

8)s2

+ 2t5u5(t+ u)

3(138t

6+ 635ut

5+ 1406u

2t4

+ 1938 u3t3

+ 1431u4t2

+ 633u5t+ 159u

6)s+ 3t

6u6(t+ u)

4(22 t

4+ 48ut

3+ 71u

2t2

+46u3t+23u

4))H(1, 0, 1, z)−18s

2t2

(s+t)3u2((

11t6−30ut

5+213u

2t4−312u

3t3

+267u4t2

+18u5t+25u

6)s13

+(31t

7−410ut6

−369u2t5−2238 u

3t4−3629u

4t3

+ 882u5t2−157u

6t+ 162u

7)s12

+ 6(4 t

8−169ut7−548u

2t6−1214u

3t5−3540u

4t4−2423u

5t3

+6u6t2−194u

7t+78u

8)s11−2

(8t

9+525ut

8+3009u

2t7

+6178 u3t6

+20238u4t5

+34836u5t4

+15637u6t3

+2622u7t2

+1500u8t

−409u9)s10−

(47t

10+414ut

9+4737u

2t8

+13612u3t7

+40505u4t6

+122994u5t5

+134809u6t4

+47600u7t3

+14496u8t2

+3932u9t

−1002u10)s9−3

(13t

11−178ut10−49u

2t9

+3534u3t8

+11835u4t7

+41126u5t6

+79799u6t5

+58892u7t4

+19400u8t3

+7200u9t2

= + 946u10t− 310u

11)s8 − 2

(6 t

12 − 513ut11 − 2157u

2t10

+ 378u3t9

+ 12324u4t8

+ 38742u5t7

+ 106815u6t6

+ 143160u7t5

+ 82758u8t4

+ 31963u9t3

+ 11604u10

t2

+ 654u11t− 326u

12)s7

+ 2u(295t

12+ 1920u t

11+ 4830u

2t10

+ 6204u3t9

+ 5961u4t8

− 24411u5t7 − 100874u

6t6 − 120402u

7t5 − 71423u

8t4 − 33991u

9t3 − 9972u

10t2 − 344u

11t + 159u

12)s6

+ 3u(32t

13+ 350ut

12

+ 3168u2t11

+ 13042u3t10

+ 29184u4t9

+ 33896u5t8 − 4056u

6t7 − 58669u

7t6 − 65010u

8t5 − 40423u

9t4 − 18184u

10t3

− 4103u11t2 − 170u

12t+ 31u

13)s5

+ u2(− 48t

13+ 3608ut

12+ 25530u

2t11

+ 71904u3t10

+ 106376u4t9

+ 63966u5t8 − 61287u

6t7

− 145806 u7t6− 123813u

8t5− 69894u

9t4− 26949u

10t3− 5154u

11t2− 333 u

12t+ 12u

13)s4

+ 2tu3(266t

12+ 2617ut

11+ 9639 u

2t10

+ 17909u3t9

+ 17090u4t8 − 312u

5t7 − 23751u

6t6 − 31075u

7t5 − 23124u

8t4 − 12753u

9t3 − 4496u

10t2 − 834u

11t− 72 u

12)s3

− 6tu4(t + u)

2(17t

10 − 71ut9 − 381u

2t8 − 637 u

3t7 − 293u

4t6

+ 591u5t5

+ 705u6t4

+ 627u7t3

+ 256u8t2

+ 50u9t + 4u

10)s2

+ t2u5(t + u)

3(48t

8+ 428ut

7+ 828u

2t6

+ 573 u3t5 − 481u

4t4 − 687u

5t3 − 585u

6t2 − 198u

7t− 30u

8)s− t3 u6

(t + u)6(14t

4

+ 12ut3

+ 21u2t2

+ 12u3t + 14u

4))

H(2, 1, 0, y)− 18s2t2u2(t + u)

2((

83t4

+ 224ut3

+ 312u2t2

+ 224u3t + 83u

4)s16

+(646t

5

+ 2236ut4

+ 3738u2t3

+ 3738u3t2

+ 2236u4t + 646u

5)s15

+ 3(795t

6+ 3434u t

5+ 6735u

2t4

+ 8252u3t3

+ 6735u4t2

+ 3434u5t

+ 795u6)s14

+(5590t

7+ 29722ut

6+ 68154u

2t5

+ 96362u3t4

+ 96362u4t3

+ 68154u5t2

+ 29722u6t + 5590u

7)s13

+(9297t

8

= + 59792u t7

+ 162893u2t6

+ 265856u3t5

+ 307366u4t4

+ 265856u5t3

+ 162893u6t2

+ 59792u7t + 9297u

8)s12

+ 6(1912t

9

+ 14697ut8

+ 48146 u2t7

+ 92627u3t6

+ 123322u4t5

+ 123322u5t4

+ 92627u6t3

+ 48146u7t2

+ 14697u8t + 1912u

9)s11

+(10571t

10+ 97460ut

9+ 390525 u

2t8

+ 895950u3t7

+ 1372200u4t6

+ 1560372u5t5

+ 1372200u6t4

+ 895950u7t3

+ 390525u8t2

+ 97460u9t + 10571u

10)s10

+ 2(3555t

11+ 40253ut

10+ 202415u

2t9

+ 561210u3t8

+ 989305u4t7

+ 1257298u5t6

+ 1257298u6t5

+ 989305u7t4

+ 561210u8t3

+ 202415u9t2

+ 40253u10t + 3555u

11)s9

+ 3(1100t

12+ 16144u t

11+ 105097u

2t10

+ 356156u3t9

+ 736699u4t8

+ 1061804u5t7

+ 1182566u6t6

+ 1061804u7t5

+ 736699u8t4

+ 356156u9t3

+ 105097 u10t2

+ 16144u11t+ 1100u

12)s8

+ 2(471t

13+ 10059u t

12+ 89007u

2t11

+ 370856u3t10

+ 918809u4t9

+ 1568172u5t8

+ 2010976u6t7

+ 2010976u7t6

+ 1568172u8t5

+ 918809u9t4

+ 370856 u10t3

+ 89007u11t2

+ 10059u12t + 471u

13)s7

+(124 t

14+ 5166ut

13+ 68942u

2t12

+ 360694u3t11

+ 1093775u4t10

+ 2281660u5t9

+ 3515021u6t8

+ 4060864u7t7

+ 3515021u8t6

+ 2281660u9t5

+ 1093775u10t4

+ 360694u11t3

= + 68942u12

t2

+ 5166u13t + 124u

14)s6

+ 6tu(102t

13+ 2718u t

12+ 19299u

2t11

+ 75952u3t10

+ 198691u4t9

+ 370135u5t8

+ 503605u6t7

+ 503605u7t6

+ 370135u8t5

+ 198691u9t4

+ 75952u10

t3

+ 19299u11t2

+ 2718u12t + 102u

13)s5

+ t2u2(1752 t

12

+ 21508ut11

+ 127396u2t10

+ 438996u3t9

+ 986209u4t8

+ 1559032u5t7

+ 1808388u6t6

+ 1559032u7t5

+ 986209u8t4

+ 438996 u9t3

+ 127396u10t2

+ 21508u11t + 1752u

12)s4

+ 2t3u3(834t

11+ 10755ut

10+ 52845u

2t9

+ 146657u3t8

+ 271322u4t7

+ 363015u5t6

+ 363015u6t5

+ 271322u7t4

+ 146657u8t3

+ 52845u9t2

+ 10755u10t + 834u

11)s3

+ 6t4u4(t + u)

2(283 t

8+ 1733ut

7+ 4779u

2t6

+ 8360u3t5

+ 10092u4t4

+ 8360u5t3

+ 4779u6t2

+ 1733u7t+ 283u

8)s2

+ 2t5u5(t+ u)

3(282t

6+ 1178u t

5+ 2417u

2t4

+ 3162u3t3

+ 2417u4t2

+ 1178u5t + 282u

6)s + 110 t

6u6(t + u)

4(t2

+ ut + u2)2)

H(2, 3, 2, y)

}/(27s

3t3u3(s + t)

6(s + u)

6(t + u)

6)

– 42 –

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two-loop qcd correction to massive spin-2 …prepared for submission to jhep two-loop qcd correction...

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