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Preprints, Working Papers, ... Year : 2022

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

Abstract

In this paper, we present two new representations of the alternating Zeta function. We show that for any s ∈ 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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Dates and versions

hal-03612591 , version 1 (17-03-2022)

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Serge Iovleff. A New Probabilistic Representation of the Alternating Zeta Function and a New Selberg-like Integral Evaluation. 2022. ⟨hal-03612591⟩
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