Abstract
In this article, we define an extended version of the Pochhammer symbol and then introduce the corresponding extension of the tau-Gauss hypergeometric function. The basic properties of the extended tau-Gauss hypergeometric function, including integral and derivative formulas involving the Mellin transform and the operators of fractional calculus, are derived. We also consider some new and known results as consequences of our proposed extension of the tau-Gauss hypergeometric function.