An extension of the multiple Erdélyi-Kober operator and representations of the generalized hypergeometric functions
Fecha
2018Versión
Acceso abierto / Sarbide irekia
Tipo
Artículo / Artikulua
Versión
Versión aceptada / Onetsi den bertsioa
Identificador del proyecto
Impacto
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10.1515/fca-2018-0071
Resumen
In this paper we investigate the extension of the multiple Erd elyi-Kober
fractional integral operator of Kiryakova to arbitrary complex values of parameters
by the way of regularization. The regularization involves derivatives
of the function in question and the integration with respect to a kernel
expressed in terms of special case of Meijer's G function. An action of the
regularized multi ...
[++]
In this paper we investigate the extension of the multiple Erd elyi-Kober
fractional integral operator of Kiryakova to arbitrary complex values of parameters
by the way of regularization. The regularization involves derivatives
of the function in question and the integration with respect to a kernel
expressed in terms of special case of Meijer's G function. An action of the
regularized multiple Erd elyi-Kober operator on some simple kernels leads
to decomposition formulas for the generalized hypergeometric functions. In
the ultimate section, we de ne an alternative regularization better suited
for representing the Bessel type generalized hypergeometric function p1Fp.
A particular case of this regularization is then used to identify some new
facts about the positivity and reality of zeros of this function. [--]
Materias
Multiple Erdélyi-Kober operator,
Meijer's G function,
Generalized hypergeometric function,
Hadamard finite part
Editor
De Gruyter
Publicado en
Fractional Calculus & Applied Analysis, Vol. 21, No 5 (2018), 1360–1376
Departamento
Universidad Pública de Navarra. Departamento de Ingeniería Matemática e Informática /
Nafarroako Unibertsitate Publikoa. Matematika eta Informatika Ingeniaritza Saila
Versión del editor
Entidades Financiadoras
The research of the first author has been supported by the Russian Science Foundation under the project 14-11-00022. The research of the second author has been supported by the Spanish Ministry of "Economía y Competitividad" under the project MTM2017-83490-P and by the Universidad Pública de Navarra.