Some Properties of the ( p , q ) -Fibonacci and ( p , q ) -Lucas Polynomials

Abstract

Riordan arrays are useful for solving the combinatorial sums by the help of generating functions. Many theorems can be easily proved by Riordan arrays. In this paper we consider the Pascal matrix and define a new generalization of Fibonacci polynomials called $(p,q)$-Fibonacci polynomials. We obtain combinatorial identities and by using Riordan method we get factorizations of Pascal matrix involving $(p,q)$-Fibonacci polynomials.