On Extended Transformation Formulae Associated to the k-Hypergeometric Function

Abstract

Recently the second order homogeneous k-hypergeometric differential equation and the definition of the function  as its solution at the origin have been presented. Motivated by the current research work in the study of k-hypergeometric functions, our aim is to establish certain extended transformation formulae related to the  k-hypergeometric function with the Euler's identity for  Gauss hypergeometric function as a special case.