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

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Abstract

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.

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  1. Department of Mathematical Sciences, University of Wisconsin–Milwaukee, P.O. Box 413, Milwaukee, WI, 53201, USA

    Hans Volkmer

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  1. Hans Volkmer
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Volkmer, H. Factorial series connected with the Lambert function, and a problem posed by Ramanujan. Ramanujan J 16, 235–245 (2008). https://doi.org/10.1007/s11139-007-9104-y

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  • DOI: https://doi.org/10.1007/s11139-007-9104-y

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