International Journal of Mathematics and Mathematical Sciences
Volume 2012 (2012), Article ID 182785, 14 pages
http://dx.doi.org/10.1155/2012/182785
Research Article

Some New Classes of Generalized Apostol-Euler and Apostol-Genocchi Polynomials

R. Tremblay,1 S. Gaboury,2 and B.-J. Fugère2

1Department of Mathematics and Computer Science, University of Quebec at Chicoutimi, Chicoutimi, QC, Canada G7H 2B1
2Department of Mathematics and Computer Science, Royal Military College of Canda, Kingston, ON, Canada K7K 5L0

Received 27 February 2012; Accepted 8 May 2012

Academic Editor: S. S. Dragomir

Copyright © 2012 R. Tremblay 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

The main object of this paper is to introduce and investigate two new classes of generalized Apostol-Euler and Apostol-Genocchi polynomials. In particular, we obtain a new addition formula for the new class of the generalized Apostol-Euler polynomials. We also give an extension and some analogues of the Srivastava-Pintér addition theorem obtained in the works by Srivastava and Pintér (2004) and R. Tremblay, S. Gaboury, B.-J. Fugère, and Tremblay et al. (2011). for both classes.