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Journal of Mathematics
Volume 2013 (2013), Article ID 629132, 9 pages
Research Article

General Eulerian Numbers and Eulerian Polynomials

1Department of Mathematics and Statistics, Radford University, Radford, VA 24141, USA
2Department of Decision Sciences, San Francisco State University, CA 94132, USA
3Department of Mathematics, Michigan State University, East Lansing, MI 48824, USA

Received 26 October 2012; Accepted 3 January 2013

Academic Editor: Mike Tsionas

Copyright © 2013 Tingyao Xiong 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.


We will generalize the definitions of Eulerian numbers and Eulerian polynomials to general arithmetic progressions. Under the new definitions, we have been successful in extending several well-known properties of traditional Eulerian numbers and polynomials to the general Eulerian polynomials and numbers.