A STUDY OF THE EXTENDED τ, β -GAUSS HYPERGEOMETRIC FUNCTION
BHUPENDER SINGH SHAKTAWAT *
Department of Mathematics and Statistics, Jai Narain Vyas University, Jodhpur – 342005, India
DEVENDRA SINGH RAWAT
Department of Mathematics and Statistics, Jai Narain Vyas University, Jodhpur – 342005, India
RAJEEV KUMAR GUPTA
Department of Mathematics and Statistics, Jai Narain Vyas University, Jodhpur – 342005, India
*Author to whom correspondence should be addressed.
Abstract
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.
Keywords: Generalized Pochhammer symbol, Gauss hypergeometric function, τ-Gauss hypergeometric function, Mellin transform and Fractional calculus