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Extended Laguerre Polynomials Associated with Hermite, Bernoulli, and Euler Numbers and Polynomials

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  • Taekyun Kim
  • Dae San Kim

Abstract

Let ð ð ‘› = { ð ‘ ( ð ‘¥ ) ∈ â„ [ ð ‘¥ ] ∣ d e g ð ‘ ( ð ‘¥ ) ≤ ð ‘› } be an inner product space with the inner product ∫ ⟨ ð ‘ ( ð ‘¥ ) , ð ‘ž ( ð ‘¥ ) ⟩ = ∞ 0 ð ‘¥ ð ›¼ ð ‘’ − ð ‘¥ ð ‘ ( ð ‘¥ ) ð ‘ž ( ð ‘¥ ) ð ‘‘ ð ‘¥ , where ð ‘ ( ð ‘¥ ) , ð ‘ž ( ð ‘¥ ) ∈ ð ð ‘› and ð ›¼ ∈ â„ with ð ›¼ > − 1 . In this paper we study the properties of the extended Laguerre polynomials which are an orthogonal basis for ð ð ‘› . From those properties, we derive some interesting relations and identities of the extended Laguerre polynomials associated with Hermite, Bernoulli, and Euler numbers and polynomials.

Suggested Citation

  • 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.
    • Handle: RePEc:hin:jnlaaa:957350
    DOI: 10.1155/2012/957350
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    Cited by:

    1. 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.
    2. 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.
    3. 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.

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