Some results on k-hypergeometric function

Abstract

In this paper, we establish integral representation and differentiation formulas for k-Gauss hypergeometric function 2F1,k(a, b; c; z) and develops a relationship with k-Confluent hypergeometric function 1F1,k(a, b; c; z), which are based properties defined by Rao and Shukla. Our study is to identify the integral as well differential representation of 2F1,k(a, b; c; z) and also find the inverse Laplace transform on it.