Integral representation and computational properties of the incomplete Fox-Wright function

The main focus of this paper is to investigate some new properties of the incomplete Fox-Wright function. We derive an integral representation of the incomplete Fox-Wright function whose terms contain Fox's H-function. As a direct consequence, it leads to some new results including inequalities, log-convexity and complete monotonicity for this function. Moreover, it yields interesting monotonicity involving the ratios of the incomplete Fox-Wright function. Furthermore, certain generating functions for the incomplete Fox-Wright function when their terms contain the Appell function of the first kind are established. Finally, by means of the generating functions obtained here, new summation formula for the incomplete Fox-Wright function in terms of the H-function of two variables is made.

Automated summary

This paper investigates some new properties of the incomplete Fox-Wright function, including integral representation, inequalities, log-convexity, and complete monotonicity. It also establishes generating functions related to the Appell function of the first kind and provides new summation formula for the incomplete Fox-Wright function using these generating functions.