## Journal of Applied Mathematics

### 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.

#### Article information

Source
J. Appl. Math., Volume 2012 (2012), Article ID 264842, 18 pages.

Dates
First available in Project Euclid: 14 December 2012

https://projecteuclid.org/euclid.jam/1355495287

Digital Object Identifier
doi:10.1155/2012/264842

Mathematical Reviews number (MathSciNet)
MR2970424

Zentralblatt MATH identifier
1278.11017

#### Citation

Lee, GwangYeon; Asci, Mustafa. Some Properties of the $(p,q)$ -Fibonacci and $(p,q)$ -Lucas Polynomials. J. Appl. Math. 2012 (2012), Article ID 264842, 18 pages. doi:10.1155/2012/264842. https://projecteuclid.org/euclid.jam/1355495287