On P,q-binomial Coefficients

In this paper, we develop the theory of a p, q-analogue of the binomial coefficients. Some properties and identities parallel to those of the usual and q-binomial coefficients will be established including the triangular, vertical, and the horizontal recurrence relations, horizontal generating function, and the orthogonality and inverse relations. The construction and derivation of these results give us an idea of how to handle complex computations involving the parameters p and q. This may be a good start in developing the theory of p, q-analogues of some special numbers in combinatorics. Furthermore, several interesting special cases will be disclosed which are analogous to some established identities of the usual binomial coefficients.