The Ramanujan Journal

, Volume 16, Issue 3, pp 235–245 | Cite as

Factorial series connected with the Lambert function, and a problem posed by Ramanujan

  • Hans Volkmer


Ramanujan’s sequence {y n } n=0 defined by \(\sum _{j=0}^{n-1}\frac{n^{j}}{j!}+\frac{n^{n}}{n!}y_{n}=\frac{e^{n}}{2}\) is expanded in factorial series derived from a series representing the Lambert W function. As a corollary, it is shown that the sequence {y n } is completely monotonic.


Lambert function Ramanujan’s conjecture Factorial series Gamma function 

Mathematics Subject Classification (2000)

33E20 33A15 


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Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.Department of Mathematical SciencesUniversity of Wisconsin–MilwaukeeMilwaukeeUSA

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