Advances in Difference Equations (Jan 2011)

<it>q</it>-Bernoulli numbers and <it>q</it>-Bernoulli polynomials revisited

  • Kim Taekyun,
  • Lee Byungje,
  • Ryoo Cheon

Journal volume & issue
Vol. 2011, no. 1
p. 33

Abstract

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Abstract This paper performs a further investigation on the q-Bernoulli numbers and q-Bernoulli polynomials given by Acikgöz et al. (Adv Differ Equ, Article ID 951764, 9, 2010), some incorrect properties are revised. It is point out that the generating function for the q-Bernoulli numbers and polynomials is unreasonable. By using the theorem of Kim (Kyushu J Math 48, 73-86, 1994) (see Equation 9), some new generating functions for the q-Bernoulli numbers and polynomials are shown. Mathematics Subject Classification (2000) 11B68, 11S40, 11S80

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