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

Taekyun Kim and Dae San Kim

Abstract and Applied Analysis, 2012, vol. 2012, 1-15

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.

Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:957350

DOI: 10.1155/2012/957350

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