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JOURNALS // Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki // Archive

Zh. Vychisl. Mat. Mat. Fiz., 2021 Volume 61, Number 10, Page 1618 (Mi zvmmf11301)

Ordinary differential equations

Generating functions involving the Fox–Wright functions

Khaled Mehrez

Departement de Mathematiques, Faculte de Sciences de Tunis, Universite Tunis El Manar, Tunis, Tunisia

Abstract: Our aim in this paper is to present several generating functions for some classes of functions associated to the Fox–Wright functions. In particular, certain generating functions for a class of function involving the Fox–Wright functions will be expressed in terms of the H-function of two variables are investigated. As applications, some generating functions associated to the generalized Mathieu type power series and the extended Hurwitz–Lerch zeta function are established. Furthermore, some new double series identity are considered.

Key words: Fox–Wright function, Fox $H$-function, hypergeometric function, Hurwitz–Lerch zeta function, generating functions.

UDC: 517.923

Received: 12.12.2020
Revised: 12.12.2020
Accepted: 09.06.2021

DOI: 10.31857/S0044466921100112


 English version:
Computational Mathematics and Mathematical Physics, 2021, 61:10, 1590–1602

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© Steklov Math. Inst. of RAS, 2024