Complete sum of products of (h,q)-extension of Euler polynomials and numbers

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Abstract
By applying the symmetry of the fermionic p-adic q-integral on , 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 at negative integers.

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