Note on q-Extensions of Euler Numbers and Polynomials of Higher Order
© Taekyun Kim et al. 2008
Received: 1 November 2007
Accepted: 22 December 2007
Published: 24 December 2007
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 . By applying their generating functions, they derived the complete sums of products of the twisted (h, q)-extension of Euler polynomials and numbers. In this paper, 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. 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 .
To access the full article, please see PDF.
This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.