# Euler Numbers and Polynomials Associated with Zeta Functions

## Related Articles

- On the q-Extension of Apostol-Euler Numbers and Polynomials. Young-Hee Kim; Wonjoo Kim; Lee-Chae Jang // Abstract & Applied Analysis;2008, p1
Recently, Choi et al. (2008) have studied the q-extensions of the Apostol-Bernoulli and the Apostol-Euler polynomials of order n and multiple Hurwitz zeta function. In this paper, we define Apostol's type q-Euler numbers En,q,Î¾ and q-Euler polynomials En,q,Î¾(x). We obtain the generating...

- A Note on Interpolation Functions of the Frobenious-Euler Numbers. Cangül, İ. N.; Simsek, Y. // AIP Conference Proceedings;11/26/2010, Vol. 1301 Issue 1, p59
The main purpose of this paper is to construct partial twisted zeta-type function, which interpolates q-generalized Frobenius-Euler numbers and twisted q-generalized Frobenius-Euler numbers. We give some applications related to this function.

- New Approach to ÷”—ž-Euler Numbers and Polynomials. Taekyun Kim; Lee-Chae Jang; Young-Hee Kim; Seog-Hoon Rim // Advances in Difference Equations;2010, Special section p1
No abstract available.

- CALCULATING ZEROS OF THE TWISTED EULER POLYNOMIALS. Agarwal, R. P.; Young-Ho Kim; Ryoo, C. S. // Neural, Parallel & Scientific Computations;Dec2008, Vol. 16 Issue 4, p505
The article attempts to calculate zeros of the twisted Euler polynomials. It analyzes the twisted Euler numbers En,w and polynomials En,w(x). It describes the zeros of the twisted Euler polynomials using a numerical investigation. It also shows the distribution and structure of the zeros of the...

- Note on q-Extensions of Euler Numbers and Polynomials of Higher Order. Taekyun Kim; Lee-Chae Jang; Cheon-Seoung Ryoo // Journal of Inequalities & Applications;2008, Vol. 2008, p1
The article presents research on the q-extensions of Euler numbers and polynomials of higher order. It investigates the Barnes-type q-Euler zeta functions and derive new formula for sums of products of q-Euler numbers and polynomials. It notes that some interesting identities were derived from...

- Zeros of Analytic Continued q-Euler Polynomials and q-Euler Zeta Function. Ryoo, C. S. // Journal of Applied Mathematics;2014, p1
We study that the q-Euler numbers En, q and q-Euler polynomials En, q(x) are analytic continued to Eq(s) and Eq(s,Ï‰).We investigate the new concept of dynamics of the zeros of analytic continued polynomials. Finally, we observe an interesting phenomenon of "scattering" of the zeros of...

- Multiple Twisted q-Euler Numbers and Polynomials Associated with p-Adic q-Integrals. Lee-Chae Jang // Advances in Difference Equations;2008, p1
By using p-adic q-integrals on â„¤p, we define multiple twisted q-Euler numbers and polynomials. We also find Witt's type formula for multiple twisted q-Euler numbers and discuss some characterizations of multiple twisted q-Euler Zeta functions. In particular, we construct multiple twisted...

- Some relationship between q-Bernstein polynomials and extended q-Euler numbers. Kim, T.; Lee, B.; Ryoo, C. S. // Journal of Computational Analysis & Applications;Apr2012, Vol. 14 Issue 3, p507
Recently several authors are studying in the area of (h, q)-Euler numbers and polynomials. In this paper we study some identities on the (h, q)-Euler numbers and polynomials related to q-Bernstein polynomials by using fermionic q-integral on Zp.

- ON THE q-EXTENSION OF THE TWISTED GENERALIZED EULER NUMBERS AND POLYNOMIALS ATTACHED TO ?. Kim, Y. H.; Lee, B.; Kim, T. // Journal of Computational Analysis & Applications;Nov2011, Vol. 13 Issue 7, p1208
In this paper, we study the generating function for the twisted generalized q-Euler numbers and polynomials attached to Dirichlet's character X and we derive some interesting identities related to these numbers and polynomials.