Publication:
Representations of hypergeometric functions for arbitrary parameter values and their use

Date

2017

Authors

Director

Publisher

Acceso abierto / Sarbide irekia
Artículo / Artikulua
Versión enviada / Bidali den bertsioa

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Abstract

Integral representations of hypergeometric functions proved to be a very useful tool for studying their properties. The purpose of this paper is twofold. First, we extend the known representations to arbitrary values of the parameters and show that the extended representations can be interpreted as examples of regularizations of integrals containing Meijer's G function. Second, we give new applications of both, known and extended representations. These include: inverse factorial series expansion for the Gauss type function, new information about zeros of the Bessel and Kummer type functions, connection with radial positive de nite functions and generalizations of Luke's inequalities for the Kummer and Gauss type functions.

Description

Esta es la versión no revisada del artículo: D.B. Karp, J.L. López, Representations of hypergeometric functions for arbitrary parameter values and their use, Journal of Approximation Theory, Volume 218, 2017, Pages 42-70, ISSN 0021-9045. Se puede consultar la versión final en https://doi.org/10.1016/j.jat.2017.03.004.

Keywords

Generalized hypergeometric function, Meijer's G function, Integral representation, Radial positive de nite function, Inverse factorial series, Hadamard nite part

Department

Ingeniería Matemática e Informática / Matematika eta Informatika Ingeniaritza

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