Abstract and Applied Analysis
Volume 2011 (2011), Article ID 123483, 9 pages
http://dx.doi.org/10.1155/2011/123483
Research Article

Some Identities of the Twisted 𝑞 -Genocchi Numbers and Polynomials with Weight 𝛼 and 𝑞 -Bernstein Polynomials with Weight 𝛼

H. Y. Lee, N. S. Jung, and C. S. Ryoo

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

Received 7 July 2011; Accepted 22 August 2011

Academic Editor: John Rassias

Copyright © 2011 H. Y. Lee 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

Recently mathematicians have studied some interesting relations between 𝑞 -Genocchi numbers, 𝑞 -Euler numbers, polynomials, Bernstein polynomials, and 𝑞 -Bernstein polynomials. In this paper, we give some interesting identities of the twisted 𝑞 -Genocchi numbers, polynomials, and 𝑞 -Bernstein polynomials with weighted 𝛼 .