Representations of two parameter quantum algebras and p, q-special functions

In this paper, the connection between p, q-analogue of special functions and representations of certain two parameter quantum algebras has been developed. The realizations of the representations of these quantum algebras are in terms of p, q-derivative operators. The matrix elements of these representations are computed in terms of the generalized p, q-hypergeometric series. This leads to the developments in the theory of p, q-special functions. © 2007 Elsevier Inc. All rights reserved.