Abstract and Applied Analysis

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

Taekyun Kim and Dae San Kim

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Abstract

Let P n = { p ( x ) [ x ] deg p ( x ) n } be an inner product space with the inner product p ( x ) , q ( x ) = 0 x α e - x p ( x ) q ( x ) d x , where p ( x ) , q ( x ) P n and α with α > - 1 . In this paper we study the properties of the extended Laguerre polynomials which are an orthogonal basis for P n . From those properties, we derive some interesting relations and identities of the extended Laguerre polynomials associated with Hermite, Bernoulli, and Euler numbers and polynomials.

Article information

Source
Abstr. Appl. Anal., Volume 2012 (2012), Article ID 957350, 15 pages.

Dates
First available in Project Euclid: 14 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1355495855

Digital Object Identifier
doi:10.1155/2012/957350

Mathematical Reviews number (MathSciNet)
MR2969990

Zentralblatt MATH identifier
1258.33006

Citation

Kim, Taekyun; Kim, Dae San. Extended Laguerre Polynomials Associated with Hermite, Bernoulli, and Euler Numbers and Polynomials. Abstr. Appl. Anal. 2012 (2012), Article ID 957350, 15 pages. doi:10.1155/2012/957350. https://projecteuclid.org/euclid.aaa/1355495855


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