Turkish Journal of Analysis and Number Theory

4

Authors: H. M. Srivastava, Rashmi Jain, M. K. Bansal

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.

12

Authors: Mehmet Acikgoz, Serkan Araci, Uğur Duran

In the year 2011, the idea of multiple q-calculus was formulated and introduced in the Ph.D. dissertation of Nalci in which this idea is simple but elegant method in order to derive new generating functions of some special polynomials that are generalizations of known q-polynomials. In this paper, we will use Nalci’s method in order to find a systematic study of new types of the Bernoulli polynomials, Euler polynomials and Genocchi polynomials. Also we will obtain recursive formulas for these polynomials.