Abstract and Applied Analysis
Volume 2011 (2011), Article ID 634675, 11 pages
Review Article

Some Identities on the ๐‘ž -Integral Representation of the Product of Several ๐‘ž -Bernstein-Type Polynomials

Department of Mathematics, Kwangwoon University, Seoul 139-701, Republic of Korea

Received 28 August 2011; Accepted 5 November 2011

Academic Editor: Pavel Drรกbek

Copyright © 2011 Taekyun Kim. 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.


The purpose of this paper is to give some properties of several ๐‘ž -Bernstein-type polynomials to express the ๐‘ž -integral on [0, 1] in terms of ๐‘ž -beta and ๐‘ž -gamma functions. Finally, we derive some identities on the ๐‘ž -integral of the product of several ๐‘ž -Bernstein-type polynomials.