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Studies in Sums of Finite Products of the Second, Third, and Fourth Kind Chebyshev Polynomials

Author

Listed:
  • Taekyun Kim

    (School of Science, Xi’an Technological University, Xi’an 710021, China
    Department of Mathematics, Kwangwoon University, Seoul 139-701, Korea)

  • Dae San Kim

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

  • Hyunseok Lee

    (Department of Mathematics, Kwangwoon University, Seoul 139-701, Korea)

  • Jongkyum Kwon

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

Abstract

In this paper, we consider three sums of finite products of Chebyshev polynomials of two different kinds, namely sums of finite products of the second and third kind Chebyshev polynomials, those of the second and fourth kind Chebyshev polynomials, and those of the third and fourth kind Chebyshev polynomials. As a generalization of the classical linearization problem, we represent each of such sums of finite products as linear combinations of Hermite, generalized Laguerre, Legendre, Gegenbauer, and Jacobi polynomials. These are done by explicit computations and the coefficients involve terminating hypergeometric functions 2 F 1 , 1 F 1 , 2 F 2 , and 4 F 3 .

Suggested Citation

  • Taekyun Kim & Dae San Kim & Hyunseok Lee & Jongkyum Kwon, 2020. "Studies in Sums of Finite Products of the Second, Third, and Fourth Kind Chebyshev Polynomials," Mathematics, MDPI, vol. 8(2), pages 1-17, February.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:2:p:210-:d:317611
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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. 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.
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