On q-Analogue and (p,q)–Analogue of Gamma and Beta Functions

ABSTRACT: In this study we discuss the integral representation of the q-analogue of two special functions, q-GF (gamma function) and q-BF (beta function). This discussion gives a very attractive q-constant.Also, we get the proof of the famous Jacobi triple product which contains the identity of Jacobi .After that we obtain a new proof for Ramanujan’s equation. Furthermore, we introduce a new generalization of gamma function and beta function that are: the (p,q) - GF and the (p,q) - BF. Finally, we obtain an equivalent definitions for (p,q) - analogue for GF and BF. Keywords: q-Gamma Function, q-Beta Function, (p,q)-Gamma Function, (p,q)-Beta Function.