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
Amritsar-143005
Punjab
India

Abstract:

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 $\sum_{n=0}^{\infty}\alpha^n n^k$, $0\vert\alpha\vert1$, $k\in\mathbb{N} _0$ 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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