Table of Contents
International Scholarly Research Notices
Volume 2014 (2014), Article ID 678408, 8 pages
http://dx.doi.org/10.1155/2014/678408
Research Article

The Translated Dowling Polynomials and Numbers

Department of Mathematics, Mindanao State University, Main Campus, 9700 Marawi City, Philippines

Received 21 October 2014; Revised 2 December 2014; Accepted 3 December 2014; Published 22 December 2014

Academic Editor: Riccardo Dondi

Copyright © 2014 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

More properties for the translated Whitney numbers of the second kind such as horizontal generating function, explicit formula, and exponential generating function are proposed. Using the translated Whitney numbers of the second kind, we will define the translated Dowling polynomials and numbers. Basic properties such as exponential generating functions and explicit formula for the translated Dowling polynomials and numbers are obtained. Convexity, integral representation, and other interesting identities are also investigated and presented. We show that the properties obtained are generalizations of some of the known results involving the classical Bell polynomials and numbers. Lastly, we established the Hankel transform of the translated Dowling numbers.