Some results on a generalized hypergeometric function

A generalized beta function and associated probability density

“…Virchenko et al [12] have treated a generalized gamma function in the form, [8]. Moreover, if we take a = 0 in this equation, we get the well-known gamma function.…”

“…Kalla and Al-Saqabi [6] have used this function to define a probability density function, which generalizes results of Kobayashi [8] and Kalla et al [7]. is the ω-Gauss hypergeometric function [12,13] whose series representation is given by, …”

“…Recently, many authors have defined and studied generalized form of different special functions [4,5,8,12,13]. Virchenko et al [12] have treated a generalized gamma function in the form, [8].…”

CERTAIN RESULTS ON EXTENDED GENERALIZED Τ-Gauss HYPERGEOMETRIC FUNCTION

“…Our results motivated mainly by investigations of the τ -Gauss hypergeometric function 2 R τ 1 (z) and 3 R τ 2 (z) (see, [3,8,10,20]). We obtained certain integral representation, a derivative formula, Integral transform and fractional calculus approach of this new extended generalized τ -Gauss hypergeometric function r F τ s (z).…”

On Certain Class of Analytic Functions Involving Linear Operators

“…Let denote the class of functions of the form , and 2 R 1 1 , α 2 ; 1 ; ; is the generalized hypergeometric function, defined by [9] 2 R 1 1 , α 2 ; 1 ; ; = Γ( 1 )…”