ON EXTENSIONS OF EXTENDED BETA AND GAUSS HYPERGEOMETRIC FUNCTIONS WITH THEIR APPLICATIONS

The Beta function and its extensions play a crucial role in the study of some special functions; several researchers have introduced and investigated various extensions of this important function. In this paper we present further extensions of the Beta and the Gauss hypergeometric functions. We also explore some of their properties, derive integral representation, and establish summation formulas. Furthermore, we investigate the relationship between these generalized Beta functions and other special functions, such as the Fox Wright function, Fox's H-function, and generalized hypergeometric function.