NOVEL CLASS OF FINITE INTEGRALS INVOLVING GENERALISED HYPERGEOMETRIC FUNCTION

The classical summation theorems like Gauss theorem, Gauss second theorem, Bailey's theorem, Kummer's theorem, Watson theorem, Dixon theorem, Whipple's theorem and Saalshutz theorem respectively for the hypergeometric series 2F1 and 3F2 play a key role in the theory of hypergeometric and generalized hypergeometric series and are widely used in many fields. In this research paper, we wish to evaluate a new class of integrals consisting of twenty five results related to generalized hypergeometric function. These twenty five results are expressed in the single integral in the form :

The results are obtained by employing generalizations of classical Watson's summation theorem previously derived by Lavoie et al. together with an Euler's beta integral. Finally, we will be obtaining fifty new integrals and few more integrals expressed in two general integrals consisting of twenty five each as special cases.