A New Probabilistic Representation of the Alternating Zeta Function and a New Selberg-like Integral Evaluation
Classical Analysis and ODEs
2022-03-21 v1 Probability
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.
Keywords
Cite
@article{arxiv.2203.09787,
title = {A New Probabilistic Representation of the Alternating Zeta Function and a New Selberg-like Integral Evaluation},
author = {Serge Iovleff},
journal= {arXiv preprint arXiv:2203.09787},
year = {2022}
}