A note on a generalisation of a definite integral involving the Bessel function of the first kind

Abstract

We consider a generalisation of a definite integral involving the Bessel function of the first kind. It is shown that this integral can be expressed in terms of the Fox-Wright function ${}_p{\Psi }_q(z)$ of one variable. Some consequences of this representation are explored by suitable choice of parameters. In addition, two closed-form evaluations of infinite series of the Fox-Wright function are deduced.

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