eng Science and Education Publishing Turkish Journal of Analysis and Number Theory 2333-1232 2015-12-03 3 5 116 119 10.12691/tjant-3-5-1 TJANT2015351 article H. M. Srivastava harimsri@math.uvic.ca 1 2 Rashmi Jain 3 M. K. Bansal 3 Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia V8W 3R4, Canada Department of Mathematics, Malaviya National Institute of Technology, Jaipur 302017, Rajasthan, India 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. http://pubs.sciepub.com/tjant/3/5/1/tjant-3-5-1.pdf S-Generalized Gauss hypergeometric function Integral representation Complex integral representation Mellin transform Integral transform Inversion formula