Reduction of a class of Fox-Wright psi functions for certain rational parameters

The Fox-Wright Psi function is a special case of Foxʹs H-function and a generalization of the generalized hypergeometric function. In the present paper, we show that the Psi function reduces to a single generalized hypergeometric function when certain of its parameters are integers and to a finite sum of generalized hypergeometric functions when these parameters are rational numbers. Applications to the solution of algebraic trinomial equations and to a problem in information theory are provided. A connection with Meijerʹs G-function is also discussed.