Representations of hypergeometric functions for arbitrary parameter values and their use
Fecha
2017Versión
Acceso abierto / Sarbide irekia
Tipo
Artículo / Artikulua
Versión
Versión enviada / Bidali den bertsioa
Impacto
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nodoi-noplumx
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Resumen
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 a ...
[++]
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. [--]
Materias
Generalized hypergeometric function,
Meijer's G function,
Integral representation,
Radial positive de nite function,
Inverse factorial series,
Hadamard nite part
Notas
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.
Departamento
Universidad Pública de Navarra. Departamento de Ingeniería Matemática e Informática /
Nafarroako Unibertsitate Publikoa. Matematika eta Informatika Ingeniaritza Saila
Entidades Financiadoras
Research of the first author (Sections 1–3) has been supported by the Russian Science Foundation
under project 14-11-0002. The research of the second author (Sections 4 and 5) has been
supported by the Spanish Ministry of Economía y Competitividad under project MTM2014-
53178.