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

In this paper our aim is to establish new integral representations for the Fox--Wright function ${}_pΨ_q[^{(α_p,A_p)}_{(β_q,B_q)}|z]$ when $μ=\sum_{j=1}^qβ_j-\sum_{k=1}^pα_k+\frac{p-q}{2}=-m,\;\;m\in\mathbb{N}_0.$ 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.

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