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International Journal of Mathematics and Mathematical Sciences
Volume 2016, Article ID 6206207, 16 pages
http://dx.doi.org/10.1155/2016/6206207
Research Article

The Noncentral Version of the Whitney Numbers: A Comprehensive Study

1Department of Mathematics, Mindanao State University, Main Campus, 9700 Marawi City, Philippines
2Department of Natural Sciences and Mathematics, Mindanao State University, Maigo School of Arts and Trades, 9206 Maigo, Philippines

Received 30 December 2015; Accepted 15 March 2016

Academic Editor: Palle E. Jorgensen

Copyright © 2016 Mahid M. Mangontarum 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

This paper is a comprehensive study of a certain generalization of Whitney-type and Stirling-type numbers which unifies the classical Whitney numbers, the translated Whitney numbers, the classical Stirling numbers, and the noncentral Stirling (or -Stirling) numbers. Several identities, applications, and occurrences are also presented.