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Representing Sums of Finite Products of Chebyshev Polynomials of the First Kind and Lucas Polynomials by Chebyshev Polynomials

Author

Listed:
  • Taekyun Kim

    (Department of Mathematics, College of Science, Tianjin Polytechnic University, Tianjin 300160, China
    Department of Mathematics, Kwangwoon University, Seoul 139-701, Korea)

  • Dae San Kim

    (Department of Mathematics, Sogang University, Seoul 121-742, Korea)

  • Dmitry V. Dolgy

    (Hanrimwon, Kwangwoon University, Seoul 139-701, Korea)

  • Jongkyum Kwon

    (Department of Mathematics Education and ERI, Gyeongsang National University, Jinju, Gyeongsangnamdo 52828, Korea)

Abstract

In this paper, we study sums of finite products of Chebyshev polynomials of the first kind and Lucas polynomials and represent each of them in terms of Chebyshev polynomials of all kinds. Here, the coefficients involve terminating hypergeometric functions 2 F 1 and these representations are obtained by explicit computations.

Suggested Citation

  • Taekyun Kim & Dae San Kim & Dmitry V. Dolgy & Jongkyum Kwon, 2018. "Representing Sums of Finite Products of Chebyshev Polynomials of the First Kind and Lucas Polynomials by Chebyshev Polynomials," Mathematics, MDPI, vol. 7(1), pages 1-15, December.
    • Handle: RePEc:gam:jmathe:v:7:y:2018:i:1:p:26-:d:193550
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    Cited by:

    1. Sergey Yekimov, 2023. "The Chebyshev Polynomials Of The First Kind For Analysis Rates Shares Of Enterprises," Papers 2307.08465, arXiv.org.

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