Journal of Integer Sequences, Vol. 19 (2016), Article 16.1.2

Defining Sums of Products of Power Sums

Jitender Singh
Department of Mathematics
Guru Nanak Dev University


We study the sums of products of power sums of positive integers and their generalizations, using the multiple products of their exponential generating functions. The generalizations include a closed form expression for the sums of products of infinite series of the form $\sum_{n=0}^{\infty}\alpha^n n^k$, $0<\vert\alpha\vert<1$, $k\in\mathbb{N} _0$ and the related Abel sum, which define, in a unified way, the sums of products of the power sums for all integers k and connect them with the zeta function.

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Received May 14 2015; revised versions received September 21 2015; September 28 2015; November 26 2015. Published in Journal of Integer Sequences, December 17 2015.

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