Some properties of hypergeometric Meixner-Pollaczek polynomials

This thesis consists of seven chapters. The first chapter is devoted to the introduction. In the second chapter, preliminaries, some definitions and lemmas used in the other chapters are given. In the third chapter, Meixner polynomials and theorems for bilinear and bilateral generating functions for these polynomials were examined. Then some recurrence relations and examined the integral representation of these polynomials. In the fourth chapter, the information about the hypergeometric Meixner-Pollaczek polynomial is given and some properties of this polynomial are given. In the fifth chapter, the theorems giving the multilinear and multilateral generating functions of this polynomial are obtained and the applications of these theorems are given. In the sixth chapter, some recurrence relations of the Meixner-Pollaczek polynomials defined in the fourth section will be given and integral representation will be obtained. In the last part, conclusions and recommendations for this thesis will be given.