AN INTEGRAL CONTAINING HYPERGEOMETRIC FUNCTION

Usha . B, Shoukat Ali

Abstract


In the theory of hypergeometric series, classical summation theorems such as those of Gauss, Gauss second, Kummer and Bailey for the series 2F1 play an important role. Whenever a hypergeometric series reduces to gamma function, the results are very important from the point of view of applications. Recently, several authors have used the above mentioned classical summation theorems in evaluating certain finite and infinite integrals involving hypergeometric function.

The aim of this short research note is to provide an integral involving hypergeometric function. The result is derived with the help of a known and very interesting and useful integral obtained earlier by Lavoie and Trottier. Some interesting special cases have also been given.


Keywords


Generalized Hypergeometric Function,Gauss’s Theorem,Single Integral

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