Science and Education Publishing Turkish Journal of Analysis and Number Theory 2333-1232 3 5 2015 12 3 A Study of the S-Generalized Gauss Hypergeometric Function and Its Associated Integral Transforms 116 119 EN H. M. Srivastava Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia V8W 3R4, Canada Rashmi Jain M. K. Bansal TJANT2015351 10.12691/tjant-3-5-1 2015 6 10 2015 10 24 2015 12 1 The aim of the present paper is to further investigate the S-generalized Gauss hypergeometric function which was recently introduced by Srivastava et al. [8]. In the course of our study, we first present an integral representation, the Mellin transform and a complex integral representation of the S-generalized Gauss hypergeometric function. Next, we introduce a new integral transform whose kernel is the S-generalized Gauss hypergeometric function and point out its three special cases which are also believed to be new. We specify that the well-known Gauss hypergeometric function transform follows as a simple special case of our integral transforms. Finally, we establish an inversion formula for the integral transform which we have introduced in this investigation.