Certain Properties and Formulae of k-Hypergeometric Functions

Abstract

Recently the second order homogeneous k-hypergeometric differential equation and the definition of the k- hypergeometric function as its solution at the origin have been presented. In this paper, we expound on the certain properties of the above function. The main object of this paper is to establish certain transformation formulae for the above function. In addition, the various important differential formulae for the k-hypergeometric functions are investigated. Since the result derived here are general in nature,