New integral representations for the Fox-Wright functions and its applications

[摘要] Our aim in this paper is to derive several new integral representations for the Fox-Wright functions. In particular, we give new Laplace and Stieltjes transforms for this special function under some restrictions on parameters. From the positivity conditions on the weight in these representations, we found sufficient conditions to be imposed on the parameters of the Fox-Wright functions which allow us to conclude that it is completely monotonic. As applications, we derive a class of functions that are related to the Fox H-functions and are positive definite. Moreover, we extended the Luke's inequalities and we establish new Arran 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. (C) 2018 Elsevier Inc. All rights reserved.

[发布日期] 2018-12-15

[关键词] Fox-Wright function;Fox's H-function;Complete monotonicity;Turan type inequalities;Generalized Stieltjes function;Mathieu-type series