A NOTE ON THE q-ANALOGUES OF EULER NUMBERS AND POLYNOMIALS

• Journal title : Honam Mathematical Journal
• Volume 33, Issue 4,  2011, pp.529-534
• Publisher : The Honam Mathematical Society
• DOI : 10.5831/HMJ.2011.33.4.529
Title & Authors
A NOTE ON THE q-ANALOGUES OF EULER NUMBERS AND POLYNOMIALS
Choi, Jong-Sung; Kim, Tae-Kyun; Kim, Young-Hee;

Abstract
In this paper, we consider the q-analogues of Euler numbers and polynomials using the fermionic p-adic invariant integral on $\small{\mathbb{Z}_p}$. From these numbers and polynomials, we derive some interesting identities and properties on the q-analogues of Euler numbers and polynomials.
Keywords
Language
English
Cited by
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Kyungpook mathematical journal, 2012. vol.52. 3, pp.299-306
2.
SYMMETRIC IDENTITIES INVOLVING WEIGHTED q-GENOCCHI POLYNOMIALS UNDER S4,DURAN, UGUR;ACIKGOZ, MEHMET;ARACI, SERKAN;

Proceedings of the Jangjeon Mathematical Society, 2015. vol.18. 4, pp.455-465
1.
On the von Staudt–Clausen's theorem related to q-Frobenius–Euler numbers, Journal of Number Theory, 2016, 159, 329
2.
Some Identities on the High-Order -Euler Numbers and Polynomials with Weight 0, Abstract and Applied Analysis, 2013, 2013, 1
3.
A NOTE ON EULERIAN POLYNOMIALS OF HIGHER ORDER, Journal of the Chungcheng Mathematical Society, 2013, 26, 1, 191
4.
A note on the Analogue of Lebesgue-Radon-Nikodym theorem with respect to weighted p-adic q-measure on Zp, Journal of Inequalities and Applications, 2013, 2013, 1, 15
References
1.
L. Carlitz, q-Bernstein numbers and polynomials, Duke Math. J. 15 (1948), 987- 1000.

2.
K. W. Hwang, D. V. Dolgy, T. Kim, S. H. Lee, On the higher-Order q-Euler numbers and polynomials with weight $\alpha$, Discrete Dynamics in Nature and Society 2011 (2011), Article ID 354329, 12 pages.

3.
T. Kim, B. Lee, J. Choi, Y. H. Kim, S. H. Rim, On the q-Euler numbers and weighted q-Bernstein polynomials, Adv. Stud. Contemp. Math. 21 (2011), 13-18.

4.
T. Kim, Some identities on the q-Euler polynomials of higher order and q-Stirling numbers by the fermionic p-adic integral on ${\mathbb{Z}_P}$, Russ. J. Math. Phys. 16 (2009), 484-491.

5.
T. Kim, A note on q-Bernstein polynomials, Russ. J. Math. Phys. 18 (2011), 73-82.

6.
M. Can, M. Genkci, V. Kurt, Y. Simsek, Twisted Dedekind type sums associated with Barnes' type multiple Frobenius-Euler l-functions, Adv. Stud. Contemp. Math. 18 (2009), 135-160.

7.
A. Bayad, Modular properties of elliptic Bernoulli and Euler functions, Adv. Stud. Contemp. Math. 20 (2010), 389-401.

8.
Q.-M. Luo, q-analogues of some results for the Apostol-Euler polynomials, Adv. Stud. Contemp. Math. 20 (2010), 103-113.

9.
D. Ding, J. Yang Some identities related to the Apostol-Euler and Apostol- Bernoulli polynomials, Adv. Stud. Contemp. Math. 20 (2010), 7-21.

10.
T. Kim, The modified q-Euler numbers and polynomials, Adv. Stud. Contemp. Math. 16 (2008), 161-170.

11.
T. Kim, A note on p-adic q-integral on ${\mathbb{Z}_P}$ associated with q-Euler numbers, Adv. Stud. Contemp. Math. 15 (2007), 133-137.

12.
C. S. Ryoo, On the generalized Barnes type multiple q-Euler polynomials twisted by ramified roots of unity, Proc. Jangjeon Math. Soc. 13 (2010), 255-263.

13.
S.-H. Rim, S. J. Lee, E. J. Moon, J. H. Jin, On the q-Genocchi numbers and poly- nomials associated with q-zeta function, Proc. Jangjeon Math. Soc. 12 (2009), 261-267.