Abstract
In this research note, an interesting integral involving hypergeometric function has been evaluated in terms of gamma function. It is further used to evaluate an integral involving product of two generalized hypergeometric functions. A few very interesting special cases have also been given
Highlights
Expressing 2F1 as a series, change the order of integration, which is seen to be justified due to uniform convergence of the series involved in the process, we have
An interesting integral involving product of two generalized hypergeometric function has been evaluated in terms of gamma function
We shall evaluate the integral involving product of two generalized hypergeometric function given in the following theorem
Summary
From (1.4), we shall first evaluate the following integral involving hypergeometric function which is believed to be new. Denoting the left-hand side of (1.5) by I, we have π a, I = e2icθ(sin θ)c−1(cos θ)c−1 2F1 Expressing 2F1 as a series, change the order of integration, which is seen to be justified due to uniform convergence of the series involved in the process, we have Evaluating the integral with the help of the following well known integral due to MacRobert [6]
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