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

Abstract

In this paper our aim is to establish new integral representations for the Fox--Wright function ${}_p{\Psi }_q{[}_{({\beta }_q,B_q)}^{({\alpha }_p,A_p)}|z]$ 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.