Generating functions of the (h, q) extension of twisted Euler polynomials and numbers

Abstract

By using p-adic q-deformed fermionic integral on Z(p), we construct new generating functions of the twisted (h, q)-Euler numbers and polynomials attached to a Dirichlet character x. By applying Mellin transformation and derivative operator to these functions; we define twisted (h, q)-extension of zeta functions and 1-functions, which interpolate the twisted (h, q)-extension of Euler numbers at negative integers. Moreover, we construct the partially twisted (h, q)-zeta function. We give some relations between the partially twisted (h, q)-zeta function and twisted (h, q)-extension of Euler numbers.