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

Abstract 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 ) -L-function, 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.