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Representing by Orthogonal Polynomials for Sums of Finite Products of Fubini Polynomials

Author

Listed:
  • Dae San Kim

    (Department of Mathematics, Sogang University, Seoul 04107, Korea)

  • Dmitry V. Dolgy

    (Kwangwoon Institute for Advanced Studies, Kwangwoon University, Seoul 01897, Korea)

  • Dojin Kim

    (Department of Mathematics, Pusan National University, Busan 46241, Korea)

  • Taekyun Kim

    (Department of Mathematics, Kwangwoon University, Seoul 01897, Korea)

Abstract

In the classical connection problem, it is dealt with determining the coefficients in the expansion of the product of two polynomials with regard to any given sequence of polynomials. As a generalization of this problem, we will consider sums of finite products of Fubini polynomials and represent these in terms of orthogonal polynomials. Here, the involved orthogonal polynomials are Chebyshev polynomials of the first, second, third and fourth kinds, and Hermite, extended Laguerre, Legendre, Gegenbauer, and Jabcobi polynomials. These representations are obtained by explicit computations.

Suggested Citation

  • Dae San Kim & Dmitry V. Dolgy & Dojin Kim & Taekyun Kim, 2019. "Representing by Orthogonal Polynomials for Sums of Finite Products of Fubini Polynomials," Mathematics, MDPI, vol. 7(4), pages 1-16, March.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:4:p:319-:d:218181
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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. Guohui Chen & Li Chen, 2018. "Some Identities Involving the Fubini Polynomials and Euler Polynomials," Mathematics, MDPI, vol. 6(12), pages 1-6, December.
    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.
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    Cited by:

    1. Waleed Mohamed Abd-Elhameed & Badah Mohamed Badah, 2021. "New Approaches to the General Linearization Problem of Jacobi Polynomials Based on Moments and Connection Formulas," Mathematics, MDPI, vol. 9(13), pages 1-28, July.

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