JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS, cilt.16, sa.11, ss.1331-1348, 2010 (SCI-Expanded)
By applying the symmetry of the fermionic p-adic q-integral on [image omitted], which is defined by T. Kim, J. Difference Equ. Appl. 14(12) (2008), pp. 1267-1277, we give recurrence identities (h, q)-Euler polynomials and the alternating sums of powers of consecutive (h, q)-integers. By using the fermionic p-adic q-integral and multinomial theorem, we construct generating functions of the higher-order (h, q)-extension of Euler polynomials and numbers. By using these numbers and polynomials, we give new approach to the complete sums of products of (h, q)-extension of Euler polynomials and numbers. We define some identities involving (h, q)-extension of Euler polynomials and numbers. Furthermore, by applying derivative operator to the generating function of the (h, q)-Euler polynomials of higher-order, we construct Barnes' type multiple (h, q)-Euler zeta function. This function interpolates (h, q)-Euler polynomials of higher-order at negative integers. We also define multiple partial (h, q)-Euler zeta function which interpolates the numbers [image omitted] at negative integers.