An extension of F1, F2, F3 appell's hypergeometric functions

Abstract

The main aim of this paper is to construct an extension of Appell's hypergeometric functions by means of modified Beta functions B(x,y;p). We give integral representations for these functions and obtain some relations for these functions and extended Gauss hypergeometric function via decomposition operators defined by Burchnall and Chaundy. Furthermore we present some transformation formulas for the first and second kind of extended Appell's hypergeometric functions. Also, we give some relations between first kind of extended Appell's hypergeometric functions.Whittaker and Modified Bessel functions.