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

S A Dar, M Kamarujjama, R B Paris

Published 2022-05-06Version 1

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.