Journal of Applied Mathematics
Volume 2012 (2012), Article ID 264842, 18 pages
http://dx.doi.org/10.1155/2012/264842
Research Article

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

GwangYeon Lee1 and Mustafa Asci2

1Department of Mathematics, Hanseo University, Seosan, Chungnam 356-706, Republic of Korea
2Department of Mathematics, Science and Arts Faculty, Pamukkale University, Denizli, Turkey

Received 23 May 2012; Revised 10 July 2012; Accepted 11 July 2012

Academic Editor: Shan Zhao

Copyright © 2012 GwangYeon Lee and Mustafa Asci. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.