# On the q-Extension of Apostol-Euler Numbers and Polynomials

## Related Articles

- Multivariate p-Adic Fermionic q-Integral on â„¤p and Related Multiple Zeta-Type Functions. Min-Soo Kim; Taekyun Kim; Jin-Woo Son // Abstract & Applied Analysis;2008, p1
In 2008, Jang et al. constructed generating functions of the multiple twisted Carlitz's type q-Bernoulli polynomials and obtained the distribution relation for them. They also raised the following problem: "are there analytic multiple twisted Carlitz' type q-zeta functions which interpolate...

- Euler Numbers and Polynomials Associated with Zeta Functions. Taekyun Kim // Abstract & Applied Analysis;2008, p1
For s Ïµ â„‚, the Euler zeta function and the Hurwitz-type Euler zeta function are defined by Î¶E(s) = 2Î£n=1âˆž((-1)n / ns, and Î¶E(s, x) = 2Î£n=0âˆž((-1)n / (n + x)s). Thus, we note that the Euler zeta functions are entire functions in whole complex s-plane, and these zeta...

- Some Identities on the Generalized q-Bernoulli, q-Euler, and q-Genocchi Polynomials. Daeyeoul Kim; Kurt, Burak; Kurt, Veli // Abstract & Applied Analysis;2013, p1
Mahmudov (2012, 2013) introduced and investigated some q-extensions of the q-Bernoulli polynomials í”…(É‘)n,q(x, y) of order É‘, the q- Euler polynomials E n,q(É‘)(x, y) of order É‘, andthe q-Genocchi polynomials G n,q(É‘)(x, y) of order É‘. In this paper, we give some...

- NOTE ON p-ADIC q-EULER MEASURE. // Journal of Computational Analysis & Applications;Jan2011, Vol. 13 Issue 1, p1329
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...

- On Interpolation Functions of the Generalized Twisted (h, q)-Euler Polynomials. Kyoung Ho Park // Journal of Inequalities & Applications;2009, Vol. 2009, Special section p1
The aim of this paper is to construct p-adic twisted two-variable Euler-(h,q)-L-functions, which interpolate generalized twisted (h,q)-Euler polynomials at negative integers. In this paper, we treat twisted (h,q)-Euler numbers and polynomials associated with p-adic invariant integral on Zp. We...

- Some identities on the second kind Bernoulli polynomials of order Î± and second kind Euler polynomials of order Î±. Kurt, Burak // AIP Conference Proceedings;Sep2012, Vol. 1479 Issue 1, p352
In this study, we gave some relations on the second kind Bernoulli polynomials and the second kind Euler polynomials. We proved two theorems on the second kind Bernoulli polynomials. Also, we gave some relations between the second kind Bernoulli polynomials and the second kind Euler polynomials.