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Expressing Sums of Finite Products of Chebyshev Polynomials of the Second Kind and of Fibonacci Polynomials by Several Orthogonal 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)

  • Jongkyum Kwon

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

  • Dmitry V. Dolgy

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

Abstract

This paper is concerned with representing sums of the finite products of Chebyshev polynomials of the second kind and of Fibonacci polynomials in terms of several classical orthogonal polynomials. Indeed, by explicit computations, each of them is expressed as linear combinations of Hermite, generalized Laguerre, Legendre, Gegenbauer and Jacobi polynomials, which involve the hypergeometric functions 1 F 1 and 2 F 1 .

Suggested Citation

  • Taekyun Kim & Dae San Kim & Jongkyum Kwon & Dmitry V. Dolgy, 2018. "Expressing Sums of Finite Products of Chebyshev Polynomials of the Second Kind and of Fibonacci Polynomials by Several Orthogonal Polynomials," Mathematics, MDPI, vol. 6(10), pages 1-14, October.
    • Handle: RePEc:gam:jmathe:v:6:y:2018:i:10:p:210-:d:176330
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    References listed on IDEAS

    as
    1. Taekyun Kim & Dae San Kim & Dmitry V. Dolgy, 2012. "Some Identities on Bernoulli and Hermite Polynomials Associated with Jacobi Polynomials," Discrete Dynamics in Nature and Society, Hindawi, vol. 2012, pages 1-11, September.
    2. Marin Marin, 2008. "Weak Solutions in Elasticity of Dipolar Porous Materials," Mathematical Problems in Engineering, Hindawi, vol. 2008, pages 1-8, September.
    3. Taekyun Kim & Dae San Kim, 2012. "Extended Laguerre Polynomials Associated with Hermite, Bernoulli, and Euler Numbers and Polynomials," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-15, September.
    Full references (including those not matched with items on IDEAS)

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