Abstract and Applied Analysis
- Abstr. Appl. Anal.
- Volume 2008 (2008), Article ID 914367, 7 pages.
On the Symmetries of the -Bernoulli Polynomials
Kupershmidt and Tuenter have introduced reflection symmetries for the -Bernoulli numbers and the Bernoulli polynomials in (2005), (2001), respectively. However, they have not dealt with congruence properties for these numbers entirely. Kupershmidt gave a quantization of the reflection symmetry for the classical Bernoulli polynomials. Tuenter derived a symmetry of power sum polynomials and the classical Bernoulli numbers. In this paper, we study the new symmetries of the -Bernoulli numbers and polynomials, which are different from Kupershmidt's and Tuenter's results. By using our symmetries for the -Bernoulli polynomials, we can obtain some interesting relationships between -Bernoulli numbers and polynomials.
Abstr. Appl. Anal., Volume 2008 (2008), Article ID 914367, 7 pages.
First available in Project Euclid: 10 February 2009
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Kim, Taekyun. On the Symmetries of the $q$ -Bernoulli Polynomials. Abstr. Appl. Anal. 2008 (2008), Article ID 914367, 7 pages. doi:10.1155/2008/914367. https://projecteuclid.org/euclid.aaa/1234298991