An Integral Involving a Generalized Hypergeometric Function

Abstract

In 1961, MacRobert in his very popular, useful and interesting research paper obtained a new type of finite integrals and used the integrals to evaluate integral involving E-functions which he had developed and is a generalization of hypergeometric and generalized hypergeometric functions. The main objective of this short research paper is to find an exciting integral associated with a generalized hypergeometric function by using the integrals obtained by MacRobert. The beauty of our results is that they appear on the product of the ratios of gamma functions. It is clear that the integral associated with gamma functions, the results are very useful from the perspective of the point of view of applications. In terms of parameters, one can easily derive the known integrals due to Rathie and the integral given in Mathai and Saxena's book. It is no exaggeration to mention here that, for other integrals, the transformation and summation formulas involve generalized hypergeometric function.