Abstract

In this paper our aim is to establish new integral representations for the Fox–Wright function \({}_{p}\Psi_{q}[^{(\alpha_{p},A_{p})}_{(\beta_{q},B_{q})}|z]\) when \(\mu=\sum_{j=1}^{q}\beta_{j}-\sum_{k=1}^{p}\alpha_{k}+\frac{p-q}{2}=-m,\;\;m\in\mathbb{N}_{0}.\) In particular, closed-form integral expressions are derived for the four parameter Wright function under a special restriction on parameters. Exponential bounding inequalities are derived for a class of the Fox–Wright function. Moreover, complete monotonicity property is presented for these functions.

中文翻译：

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Fox-Wright函数的新积分表示及其应用II

摘要

本文旨在为Fox-Wright函数\（{} _ {p} \ Psi_ {q} [^ {（\ alpha_ {p}，A_ {p}）} _ {（\ beta_ {q}，B_ {q}）} | z] \）当\（\ mu = \ sum_ {j = 1} ^ {q} \ beta_ {j}-\ sum_ {k = 1} ^ {p} \ alpha_ {k} + \ frac {pq} {2} =-m，\; \; m \ in \ mathbb {N} _ {0}。\）特别是，对于这四个变量，导出了封闭形式的整数表达式参数Wright函数受参数的特殊限制。对于一类Fox-Wright函数，导出了指数边界不等式。此外，为这些功能提供了完整的单调性。