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

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 s...

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Bibliographic Details
Main Authors: Taekyun Kim, Dae San Kim
Format: Article
Language:English
Published: Wiley 2012-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2012/957350
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Summary: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.
ISSN:1085-3375
1687-0409