Summability methods lFrom Wikipedia, the free encyclopediaIn mathematical analysis, Lambert summation is a summability method for a class of divergent series.1 DenitionA seriesan is Lambert summable to A, writtenan= A(L) , iflimr1(1 r)n=1nanrn1 rn= A.If a series is convergent to A then it is Lambert summable to A (an Abelian theorem).2 Examples n=1(n)n= 0(L) , where is the Mbius function. Hence if this series converges at all, it converges to zero.3 See alsoLambert seriesAbelPlana formulaAbelian and tauberian theorems4 ReferencesJacob Korevaar (2004). Tauberian theory. A century of developments. Grundlehren der MathematischenWissenschaften 329. Springer-Verlag. p. 18. ISBN 3-540-21058-X.Hugh L. Montgomery; Robert C. Vaughan (2007). Multiplicative number theory I. Classical theory. Cambridgetracts in advanced mathematics 97. Cambridge: Cambridge Univ. Press. pp. 159160. ISBN 0-521-84903-9.Norbert Wiener (1932). Tauberian theorems. Ann. Of Math. (The Annals of Mathematics, Vol. 33, No. 1)33 (1): 1100. doi:10.2307/1968102. JSTOR 1968102.12 5 TEXT AND IMAGE SOURCES, CONTRIBUTORS, AND LICENSES5 Text and image sources, contributors, and licenses5.1 Text Lambert summationSource: https://en.wikipedia.org/wiki/Lambert_summation?oldid=618857703 Contributors: Michael Hardy, Cris-lax, Silly rabbit, A. Pichler, Vanish2, DOI bot, Yobot, Citation bot, Citation bot 1 and Monkbot5.2 Images File:Lebesgue_Icon.svgSource: https://upload.wikimedia.org/wikipedia/commons/c/c9/Lebesgue_Icon.svgLicense: Public domainContributors: w:Image:Lebesgue_Icon.svg Original artist: w:User:James pic5.3 Content license Creative Commons Attribution-Share Alike 3.0