Abstract and Applied Analysis
Volume 2012 (2012), Article ID 865721, 12 pages
Research Article

Applications of Umbral Calculus Associated with -Adic Invariant Integrals on

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

Received 8 November 2012; Accepted 22 November 2012

Academic Editor: Gaston N'Guerekata

Copyright © 2012 Dae San Kim and Taekyun Kim. 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.


Recently, Dere and Simsek (2012) have studied the applications of umbral algebra to some special functions. In this paper, we investigate some properties of umbral calculus associated with -adic invariant integrals on . From our properties, we can also derive some interesting identities of Bernoulli polynomials.