## Abstract and Applied Analysis

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

#### Abstract

Let ${\mathbf{P}}_{n}=\{p(x)\in \Bbb R[x]\mid \mathrm{deg} p(x)\le n\}$ be an inner product space with the inner product ${\langle}p(x),q(x){\rangle}={\int }_{0}^{\infty }{x}^{\alpha }{e}^{-x}p(x)q(x)dx$, where $p(x),q(x)\in {\mathbf{P}}_{n}$ and $\alpha \in \Bbb R$ with $\alpha >-1$. In this paper we study the properties of the extended Laguerre polynomials which are an orthogonal basis for ${\mathbf{P}}_{n}$. 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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