Generating functions and integral formulas the Fox-Wright function and theirs applications

Khaled Mehrez

Published 2020-01-06Version 1

The main object of this paper is to investigate several generating functions and some integral formulas for certain 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 and new finite integral formulas of the ratios of the Fox-Wright functions are investigated. As applications, some generating functions associated to the generalized Mathieu type power series and the extended Hurwitz-Lerch zeta function and new integral formulas for some special functions are established. Furthermore, some new double series identity are considered. A conjecture about the finite Laplace transform of a class of function associated to the Fox's H-function is made.