A STUDY OF THE EXTENDED τ, β -GAUSS HYPERGEOMETRIC FUNCTION

This paper deals with the study of a new generalization of Gauss hypergeometric function. We define here an extended τ, β-Gausshypergeometric function and various properties of this new function are investigated such as its integral representation, derivative formulas and Mellin transform. Fractional calculus approach of are also established. The results presented in this paper are of general nature and results given earlier by Parmar [1], Srivastava et al. [2], Virchenko and Rumiantseva [3] and Virchenko et al. [4] follows, as special cases.