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Abstract and Applied Analysis
Volume 2013, Article ID 179841, 8 pages
http://dx.doi.org/10.1155/2013/179841
Research Article

A Generalization of Poly-Cauchy Numbers and Their Properties

1Graduate School of Science and Technology, Hirosaki University, Hirosaki 036-8561, Japan
2Department of Mathematics, Faculty of Science, Kasetsart University, Bangkok 10900, Thailand
3Institute of Mathematics and Informatics, Eszterházy Károly College, Eger 3300, Hungary

Received 23 April 2013; Revised 26 October 2013; Accepted 28 October 2013

Academic Editor: Gerd Teschke

Copyright © 2013 Takao Komatsu 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

In Komatsu's work (2013), the concept of poly-Cauchy numbers is introduced as an analogue of that of poly-Bernoulli numbers. Both numbers are extensions of classical Cauchy numbers and Bernoulli numbers, respectively. There are several generalizations of poly-Cauchy numbers, including poly-Cauchy numbers with a q parameter and shifted poly-Cauchy numbers. In this paper, we give a further generalization of poly-Cauchy numbers and investigate several arithmetical properties. We also give the corresponding generalized poly-Bernoulli numbers so that both numbers have some relations.