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International Journal of Mathematics and Mathematical Sciences
Volume 2012, Article ID 179385, 13 pages
http://dx.doi.org/10.1155/2012/179385
Research Article

Some Properties of Multiple Generalized q-Genocchi Polynomials with Weight and Weak Weight

Department of Mathematics, Hannam University, Daejeon 306-791, Republic of Korea

Received 28 May 2012; Revised 21 August 2012; Accepted 22 August 2012

Academic Editor: Cheon Ryoo

Copyright © 2012 J. Y. Kang. 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 present paper deals with the various q-Genocchi numbers and polynomials. We define a new type of multiple generalized q-Genocchi numbers and polynomials with weight α and weak weight β by applying the method of p-adic q-integral. We will find a link between their numbers and polynomials with weight α and weak weight β. Also we will obtain the interesting properties of their numbers and polynomials with weight α and weak weight β. Moreover, we construct a Hurwitz-type zeta function which interpolates multiple generalized q-Genocchi polynomials with weight α and weak weight β and find some combinatorial relations.