Discrete Dynamics in Nature and Society
Volume 2012 (2012), Article ID 619197, 10 pages
http://dx.doi.org/10.1155/2012/619197
Research Article

Some Identities on Laguerre Polynomials in Connection with Bernoulli and Euler Numbers

Dae San Kim,1 Taekyun Kim,2 and Dmitry V. Dolgy3

1Department of Mathematics, Sogang University, Seoul 121-742, Republic of Korea
2Department of Mathematics, Kwangwoon University, Seoul 139-701, Republic of Korea
3Hanrimwon, Kwangwoon University, Seoul 139-701, Republic of Korea

Received 15 May 2012; Accepted 28 June 2012

Academic Editor: Lee Chae Jang

Copyright © 2012 Dae San Kim et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We study some interesting identities and properties of Laguerre polynomials in connection with Bernoulli and Euler numbers. These identities are derived from the orthogonality of Laguerre polynomials with respect to inner product ∫ ⟨ 𝑓 , 𝑔 ⟩ = ∞ 0 𝑒 − 𝑥 2 𝑓 ( 𝑥 ) 𝑔 ( 𝑥 ) 𝑑 𝑥 .