ON THE SECOND KIND (h, q)-EULER POLYNOMIALS OF HIGHER ORDER

In this paper, we define the second kind Euler numbers E-n,q((h,k)) and polynomials E-n,q((h,k))(x) of order k. We also give the generating functions of the second kind Euler numbers and polynomials of order k. By applying the Mellin transformation to these generating functions, we construct the multiple (h, q)-Euler zeta function and Barnes' type multiple (h, q)-Euler zeta function of order k which are interpolated higher order second kind Euler numbers and polynomials at negative integers, respectively.