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New formulas including convolution, connection and radicals formulas of k-Fibonacci and k-Lucas polynomials

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  • W. M. Abd-Elhameed

    (Cairo University)

  • N. A. Zeyada

    (Cairo University
    University of Jeddah)

Abstract

This paper is dedicated to deriving some new formulas of the two classes of polynomials, namely k-Fibonacci and k-Lucas polynomials. New connection formulas between these two classes are developed. We show that the connection coefficients are expressed explicitly in terms of hypergeometric functions of the type $$_2F_{1}(z)$$ 2 F 1 ( z ) , for certain z. Some linearization formulas of the two classes of polynomials are also given. New convolution identities involving the derivatives of the two classes of k-Fibonacci and k-Lucas polynomials are derived. As an important application of employing the two classes of polynomials, reduction formulas of some odd radicals are established.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:indpam:v:53:y:2022:i:4:d:10.1007_s13226-021-00214-5
    DOI: 10.1007/s13226-021-00214-5
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    References listed on IDEAS

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    1. Falcón, Sergio & Plaza, Ángel, 2007. "On the Fibonacci k-numbers," Chaos, Solitons & Fractals, Elsevier, vol. 32(5), pages 1615-1624.
    2. W. M. Abd-Elhameed & N. A. Zeyada, 2018. "New identities involving generalized Fibonacci and generalized Lucas numbers," Indian Journal of Pure and Applied Mathematics, Springer, vol. 49(3), pages 527-537, September.
    3. Falcón, Sergio & Plaza, Ángel, 2009. "On k-Fibonacci sequences and polynomials and their derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 39(3), pages 1005-1019.
    4. 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.
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    Cited by:

    1. Waleed Mohamed Abd-Elhameed & Amr Kamel Amin, 2023. "Novel Formulas of Schröder Polynomials and Their Related Numbers," Mathematics, MDPI, vol. 11(2), pages 1-23, January.

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