SOME DEFINITE INTEGRALS INVOLVING HYPERGEOMETRIC AND GAMMA FUNCTIONS

In this article, the authors make use of the Gamma function as well as the hypergeometric functions in order to investigate and develop five definite integrals involving the elliptic integrals. The numerical approximation of these definite integrals and the corresponding hypergeometric functions are also presented. The results derived in this article are believed to be new and extend and unify those that are available in the scientific literature.