Some Definite Integrals Involving Elliptic Integrals in Association with Hypergeometric Functions

Abstract

In this paper, the authors make use of the Gamma function as well as
the hypergeometric and the generalized hypergeometric functions in order
to investigate and develop several definite integrals
involving the elliptic integrals of the first and the second kind.
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.