INTERPOLATION FUNCTIONS OF THE q-GENOCCHI AND THE q-EULER POLYNOMIALS OF HIGHER ORDER

Cangul-Ozden-Simsek [1] constructed the q-Genocchi numbers of high order using a fermionic p-adic integral on Z(p), and gave Witt's formula and the interpolation functions of these numbers. In this paper, we present the generalization of the higher order q-Euler numbers and q-Genocchi numbers of Cangul-Ozden-Simsek. We define q-extensions of omega-Euler numbers and polynomials, and omega-Genocchi numbers and polynomials of high order using the multivariate fermionic p-adic integral on Z(p). We have the interpolation functions of these numbers and polynomials. We obtain the distribution relations for q-extensions of w-Euler and w-Genocchi polynomials We also have tire interesting relation for q-extensions of these polynomials. We define (h, q)-extensions of w-Euler and w-Genocchi polynomials of high order. We have the interpolation functions for (h, q)-extensions of these polynomials. Moreover, we obtain some meaningful results of (h, q)-extensions of w-Euler and w-Genocchi polynomials.