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

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 c...

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Bibliographic Details
Published inJournal of Applied Mathematics Vol. 2012; no. 2012; pp. 890 - 907-155
Main Authors Lee, GwangYeon, Asci, Mustafa
Format Journal Article
LanguageEnglish
Published Cairo, Egypt Hindawi Limiteds 01.01.2012
Hindawi Publishing Corporation
Hindawi Limited
Wiley
Subjects
Numerical analysis
Ordinary differential equations
Polynomials
Studies
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Summary: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.
ISSN:1110-757X
1687-0042
DOI:10.1155/2012/264842