A New Probabilistic Representation of the ...
Type de document :
Pré-publication ou Document de travail
Titre :
A New Probabilistic Representation of the Alternating Zeta Function and a New Selberg-like Integral Evaluation
Auteur(s) :
Iovleff, Serge [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
MOdel for Data Analysis and Learning [MODAL]
Université de Technologie de Belfort-Montbeliard [UTBM]
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Laboratoire Paul Painlevé - UMR 8524 [LPP]
MOdel for Data Analysis and Learning [MODAL]
Université de Technologie de Belfort-Montbeliard [UTBM]
Discipline(s) HAL :
Mathématiques [math]/Analyse classique [math.CA]
Mathématiques [math]/Probabilités [math.PR]
Mathématiques [math]/Probabilités [math.PR]
Résumé en anglais : [en]
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 ...
Lire la suite >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.Lire moins >
Lire la suite >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.Lire moins >
Langue :
Anglais
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