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Some Identities Involving Fibonacci Polynomials and Fibonacci Numbers

Author

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  • Yuankui Ma

    (School of Science, Xi’an Technological University, Xi’an 710021, China)

  • Wenpeng Zhang

    (School of Science, Xi’an Technological University, Xi’an 710021, China
    School of Mathematics, Northwest University, Xi’an 710127, China)

Abstract

The aim of this paper is to research the structural properties of the Fibonacci polynomials and Fibonacci numbers and obtain some identities. To achieve this purpose, we first introduce a new second-order nonlinear recursive sequence. Then, we obtain our main results by using this new sequence, the properties of the power series, and the combinatorial methods.

Suggested Citation

  • Yuankui Ma & Wenpeng Zhang, 2018. "Some Identities Involving Fibonacci Polynomials and Fibonacci Numbers," Mathematics, MDPI, vol. 6(12), pages 1-8, December.
    • Handle: RePEc:gam:jmathe:v:6:y:2018:i:12:p:334-:d:191339
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    References listed on IDEAS

    as
    1. Xiaoxue Li, 2015. "Some Identities Involving Chebyshev Polynomials," Mathematical Problems in Engineering, Hindawi, vol. 2015, pages 1-5, March.
    2. Tingting Wang & Han Zhang, 2015. "Some Identities Involving the Derivative of the First Kind Chebyshev Polynomials," Mathematical Problems in Engineering, Hindawi, vol. 2015, pages 1-7, July.
    3. 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.
    4. Wang, Weiping & Wang, Hui, 2017. "Generalized Humbert polynomials via generalized Fibonacci polynomials," Applied Mathematics and Computation, Elsevier, vol. 307(C), pages 204-216.
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    Cited by:

    1. Dmitry Kruchinin & Vladimir Kruchinin & Yilmaz Simsek, 2020. "Generalized Tepper’s Identity and Its Application," Mathematics, MDPI, vol. 8(2), pages 1-12, February.
    2. Dongwei Guo & Wenchang Chu, 2022. "Sums of Pell/Lucas Polynomials and Fibonacci/Lucas Numbers," Mathematics, MDPI, vol. 10(15), pages 1-10, July.

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