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A common generalization of convolved generalized Fibonacci and Lucas polynomials and its applications

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  • Ye, Xiaoli
  • Zhang, Zhizheng

Abstract

The purpose of this paper is to give a common generalization of convolved generalized Fibonacci and Lucas polynomials and some recurrence relations are established. As applications, we obtain some computational formulas of mixed-multiple sums for h(x)-Fibonacci polynomials and Lucas polynomials.

Suggested Citation

  • Ye, Xiaoli & Zhang, Zhizheng, 2017. "A common generalization of convolved generalized Fibonacci and Lucas polynomials and its applications," Applied Mathematics and Computation, Elsevier, vol. 306(C), pages 31-37.
    • Handle: RePEc:eee:apmaco:v:306:y:2017:i:c:p:31-37
    DOI: 10.1016/j.amc.2017.02.016
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    References listed on IDEAS

    as
    1. Nalli, Ayse & Haukkanen, Pentti, 2009. "On generalized Fibonacci and Lucas polynomials," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 3179-3186.
    2. Falcón, Sergio & Plaza, Ángel, 2007. "On the Fibonacci k-numbers," Chaos, Solitons & Fractals, Elsevier, vol. 32(5), pages 1615-1624.
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    Cited by:

    1. Waleed Mohamed Abd-Elhameed & Andreas N. Philippou & Nasr Anwer Zeyada, 2022. "Novel Results for Two Generalized Classes of Fibonacci and Lucas Polynomials and Their Uses in the Reduction of Some Radicals," Mathematics, MDPI, vol. 10(13), pages 1-18, July.
    2. Yuankui Ma & Wenpeng Zhang, 2018. "Some Identities Involving Fibonacci Polynomials and Fibonacci Numbers," Mathematics, MDPI, vol. 6(12), pages 1-8, December.
    3. W. M. Abd-Elhameed & N. A. Zeyada, 2022. "New formulas including convolution, connection and radicals formulas of k-Fibonacci and k-Lucas polynomials," Indian Journal of Pure and Applied Mathematics, Springer, vol. 53(4), pages 1006-1016, December.
    4. Yang, Jizhen & Zhang, Zhizheng, 2018. "Some identities of the generalized Fibonacci and Lucas sequences," Applied Mathematics and Computation, Elsevier, vol. 339(C), pages 451-458.

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