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

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Listed:
  • Taekyun Kim
  • Dae San Kim

Abstract

Let Pn = {p(x) ∈ ℝ[x]∣deg p(x) ≤ n} be an inner product space with the inner product 〈p(x),q(x)〉=∫0∞xαe-xp(x)q(x)dx, where p(x), q(x) ∈ Pn and α ∈ ℝ with α > −1. In this paper we study the properties of the extended Laguerre polynomials which are an orthogonal basis for Pn. 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, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:957350
    DOI: 10.1155/2012/957350
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    References listed on IDEAS

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    1. D. S. Kim & D. V. Dolgy & T. Kim & S.-H. Rim, 2012. "Some Formulae for the Product of Two Bernoulli and Euler Polynomials," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-15, June.
    2. D. S. Kim & D. V. Dolgy & T. Kim & S.-H. Rim, 2012. "Some Formulae for the Product of Two Bernoulli and Euler Polynomials," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
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