New integral representations for the Fox-Wright functions and its applications II (1811.06352v4)

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.