Geodesic
Defining sums of products of power sums
Journal of integer sequences, Tome 19 (2016) no. 1.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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.
Classification : 11A25, 11B68, 05A10, 11B65
Keywords: power sum of integers, Bernoulli number, Bernoulli polynomial, Riemann zeta function, exponential generating function, Apostol-Bernoulli number 
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     author = {Singh, Jitender},
     title = {Defining sums of products of power sums},
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     number = {1},
     year = {2016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2016__19_1_a7/}
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Singh, Jitender. Defining sums of products of power sums. Journal of integer sequences, Tome 19 (2016) no. 1. http://geodesic.mathdoc.fr/item/JIS_2016__19_1_a7/