Note on generalized hypergeometric function

Virchenko and Rumiantseva [On the generalized associated legendre functions. Fract Cal Appl Anal. 2008; 11(2): 175- 185] gave another generalization F-2(1)tau,beta(a, b; c; z) of the hypergeometric function. In this paper, we give integral representations and differentiation formulae of F-2(1)tau,beta (a, b; c; z), alongwith relation of F-2(1)tau,beta (a, b; c; z) with the generalized Mittag-Leffler function E-alpha,beta(gamma,q)(z) [Shukla AK, Prajapati JC. On a generalization of Mittag-Leffler function and its properties. J Math Anal Appl. 2007; 336(2): 797-811.]. Further properties of the generalized hypergeometric function R-2(1)(a, b; c; t; z) [Virchenko N, Kalla SL, Al-Zamel A. Some results on a generalized hypergeometric function. Integral Transforms Spec Funct. 2001; 12(1): 89-100.], namely integral representation and differentiation formulae are also studied.