Abstract
In 2007, Ozden et al. constructed generating functions of higher-order twisted (h, q)-extension of Euler and numbers, by using p-adic, q-deformed fermionic integral on . By applying their generating functions, they derived the complete of products of the twisted (h, q)-extension of Euler and numbers. In this paper, we consider the new q-extension of Euler numbers and to be different which is treated by Ozden et al. From our q-Euler numbers and polynomials, we derive some interesting identities and we construct q-Euler zeta functions which interpolate the new q-Euler numbers and at a negative integer. Furthermore, we study Barnes-type q-Euler zeta functions. Finally, we will derive the new formula for sums of products of q-Euler numbers and polynomials by using fermionic q-adic, q-integral on .
Highlights
Introduction and notationsThroughout this paper we use the following notations
We study Barnes-type q-Euler zeta functions
By Zp we denote the ring of p-adic rational integers, Q denotes the field of rational numbers, Qp denotes the field of p-adic rational numbers, C denotes the complex number field, and Cp denotes the completion of algebraic closure of Qp
Summary
In 2007, Ozden et al constructed generating functions of higher-order twisted h, q -extension of Euler polynomials and numbers, by using p-adic, q-deformed fermionic integral on Zp. We consider the new q-extension of Euler numbers and polynomials to be different which is treated by Ozden et al From our q-Euler numbers and polynomials, we derive some interesting identities and we construct q-Euler zeta functions which interpolate the new q-Euler numbers and polynomials at a negative integer.
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