k-Srivastava hypergeometric functions

This thesis consists of five chapters. The first chapter is devoted to the introduction. In the second chapter, properties of some classical functions such as Gamma, Beta, Gaussian hypergeometric and Appell hypergeometric functions are presented. In addition, the properties of the k-generalizations of these functions and the Pochhammer k-symbol are referred. In the third chapter, the definitions of classical Srivastava hypergeometric functions are reminded. Also, the integral representations and recursion formulas of these functions are listed. The fourth chapter is the original part of the thesis. In this section, the definitions of k-Srivastava hypergeometric functions are given using the Pochhammer k-symbol. Furthermore, the relations between k-Srivastava hypergeometric functions and classical Srivastava hypergeometric functions are obtained. Then, with the help of these relations, the integral representations and recursion formulas of k-Srivastava hypergeometric functions are easily proved. In the fifth chapter, the results obtained in this thesis and the suggestions for further studies are mentioned.