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

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  • GwangYeon Lee
  • Mustafa Asci

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.

Suggested Citation

  • GwangYeon Lee & Mustafa Asci, 2012. "Some Properties of the (p, q)‐Fibonacci and (p, q)‐Lucas Polynomials," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnljam:v:2012:y:2012:i:1:n:264842
    DOI: 10.1155/2012/264842
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    References listed on IDEAS

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    1. Nalli, Ayse & Haukkanen, Pentti, 2009. "On generalized Fibonacci and Lucas polynomials," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 3179-3186.
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