A New Approach to q-Bernoulli Numbers and q-Bernoulli Polynomials Related to q-Bernstein Polynomials

作者：Acikgoz Mehmet^*; Erdal Dilek; Araci Serkan

来源：Advances in Difference Equations, 2010, 951764.

DOI：10.1155/2010/951764

We present a new generating function related to the q-Bernoulli numbers and q-Bernoulli polynomials. We give a new construction of these numbers and polynomials related to the second-kind Stirling numbers and q-Bernstein polynomials. We also consider the generalized q-Bernoulli polynomials attached to Dirichlet's character. and have their generating function. We obtain distribution relations for the q-Bernoulli polynomials and have some identities involving q-Bernoulli numbers and polynomials related to the second kind Stirling numbers and q-Bernstein polynomials. Finally, we derive the q-extensions of zeta functions from the Mellin transformation of this generating function which interpolates the q-Bernoulli polynomials at negative integers and is associated with q-Bernstein polynomials.

• 出版日期2010