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arXiv · 2203.09787

A New Probabilistic Representation of the Alternating Zeta Function and a New Selberg-like Integral Evaluation

Serge Iovleff
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Abstract

In this paper, we present two new representations of the alternating Zeta function. We show that for any s $\in$ C this function can be computed as a limit of a series of determinant. We then express these determinants as the expectation of a functional of a random vector with Dixon-Anderson density. The generalization of this representation to more general alternating series allows us to evaluate a Selberg-type integral with a generalized Vandermonde determinant.

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Serge Iovleff. 2022-03-18. A New Probabilistic Representation of the Alternating Zeta Function and a New Selberg-like Integral Evaluation. https://arxiv.org/abs/2203.09787

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