A CLASS OF HYPERGEOMETRIC GENERALIZATIONS OF AN INTEGRAL OF SRINIVASA RAMANUJAN

Abstract

The main aim of this paper is to develop some interesting applications, extensions and generalizations of Ramanujan's integral (which he obtained with the help of the celebrated Ramanujan Master theorem). Motivated essentially by some recent works by M. Garg and S. Mittal (see for example, [South East Asian J. Math. Math. Sc., 1(2) (2003), 85-95; Proc. Indian Acad. Sci. (Math. Sci.), 114(2) (2004), 99-101; Kyungpook Math. J., 44 (2004), 473-479]) and H. M. Srivastava et al. (see for example, [Rev. Roumaine Phys., 32 (1987), 685-692; Advanced Studies in Contemporary Mathematics, 18(2) (2009), 113-125]), we evaluate several general families of new definite integrals involving functions of one and more complex variables, some of which are then applied to derive the corresponding results associated with generalized Gaussian hypergeometric function qpF and the Fox-Wright generalized hypergeometric functions .