Twisted (h, q)-Bernoulli numbers and polynomials related to twisted (h, q)-zeta function and L-function

In this paper, by using q-Volkenborn integral, we construct new generating functions of the new twisted (h, q)-Bernoulli polynomials and numbers. By applying the Mellin transformation to these generating functions, we obtain integral representations of the new twisted (h, q)-zeta function and twisted (h, q)-Lfunction, which interpolate the twisted (h, q)-Bernoulli numbers and generalized twisted (h, q)-Bernoulli numbers at non-positive integers, respectively. Furthermore, relation between twisted (h, q)-zeta function and twisted (h, q)-L-function are proved. Some new relations, related to twisted (h, q)-Bernoulli polynomials and numbers, are given. © 2005 Elsevier Inc. All rights reserved.