A new extension of q-Euler numbers and polynomials related to their interpolation functions

Abstract In this work, by using a p -adic q -Volkenborn integral, we construct a new approach to generating functions of the ( h , q ) -Euler numbers and polynomials attached to a Dirichlet character χ . By applying the Mellin transformation and a derivative operator to these functions, we define ( h , q ) -extensions of zeta functions and l -functions, which interpolate ( h , q ) -extensions of Euler numbers at negative integers.