New Integral representations for the Fox-Wright functions and its applications
Abstract
Our aim in this paper is to derive several new integral representations of the Fox-Wright functions. In particular, we give new Laplace and Stieltjes transform for this special functions under a special restriction on parameters. From the positivity conditions for the weight in these representations, we found sufficient conditions to be imposed on the parameters of the Fox-Wright functions that it be completely monotonic. As applications, we derive a class of function related to the Fox H-functions is positive definite and an investigation of a class of the Fox H-function is non-negative. Moreover, we extended the Luke's inequalities and we establish a new Tur\'an type inequalities for the Fox-Wright function. Finally, by appealing to each of the Luke's inequalities, two sets of two-sided bounding inequalities for the generalized Mathieu's type series are proved.
Cite
@article{arxiv.1711.08368,
title = {New Integral representations for the Fox-Wright functions and its applications},
author = {Khaled Mehrez},
journal= {arXiv preprint arXiv:1711.08368},
year = {2017}
}