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http://dx.doi.org/10.5831/HMJ.2011.33.4.529

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

Choi, Jong-Sung (Division of General Education-Mathematics, Kwangwoon University)
Kim, Tae-Kyun (Division of General Education-Mathematics, Kwangwoon University)
Kim, Young-Hee (Division of General Education-Mathematics, Kwangwoon University)
Publication Information
Honam Mathematical Journal / v.33, no.4, 2011 , pp. 529-534 More about this Journal
Abstract
In this paper, we consider the q-analogues of Euler numbers and polynomials using the fermionic p-adic invariant integral on $\mathbb{Z}_p$. From these numbers and polynomials, we derive some interesting identities and properties on the q-analogues of Euler numbers and polynomials.
Keywords
Bernoulli numbers and polynomials; Euler numbers and polynomials; fermionic p-adic integrlal; bosonic p-adic integral;
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  • Reference
1 L. Carlitz, q-Bernstein numbers and polynomials, Duke Math. J. 15 (1948), 987- 1000.   DOI
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.   DOI
5 T. Kim, A note on q-Bernstein polynomials, Russ. J. Math. Phys. 18 (2011), 73-82.   DOI
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.