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Recently, an extension of the Pochhammer symbol was used in order to introduce and investigate a family of generalized hypergeometric functions [Srivastava et al.(2014)[11]]. The main object of this paper is to present an extension of the τ-Gauss hypergeometric functions R 1 τ 2 (z) and investigate its several properties, including, for example, its integral representations, derivative formulas, Mellin transforms and fractional calculus operators. Some interesting special cases of our main results are also pointed out.