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On the \(q\)-Euler numbers and polynomials with weight 0. (English) Zbl 1250.11027
Summary: The purpose of this paper is to investigate some properties of \(q\)-Euler numbers and polynomials with weight 0. From those \(q\)-Euler numbers with weight 0, we derive some identities on the \(q\)-Euler numbers and polynomials with weight 0.

MSC:
11B68 Bernoulli and Euler numbers and polynomials
11S80 Other analytic theory (analogues of beta and gamma functions, \(p\)-adic integration, etc.)
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[1] S. Araci, D. Erdal, and J. J. Seo, “A Study on the fermionic p-adic qintegral on \Bbb Zp associated with weighted q-Bernstein and q-Genocchi polynomials,” Abstract and Applied Analysis, vol. 2011, Article ID 649248, 10 pages, 2011. · Zbl 1269.11020 · doi:10.1155/2011/649248
[2] D. Erdal, J. J. Seo, and S. Araci, “New construction weighted (h, g)-Genocchi numbers and polynomials related to Zeta type function,” Discrete Dynamics in Nature and Society, vol. 2011, Article ID 487490, 7 pages, 2011. · Zbl 1284.11035 · doi:10.1155/2011/487490
[3] T. Kim, B. Lee, J. Choi, Y. H. Kim, and S. H. Rim, “On the q-Euler numbers and weighted q-Bernstein polynomials,” Advanced Studies in Contemporary Mathematics, vol. 21, pp. 13-18, 2011. · Zbl 1276.11033
[4] T. Kim, “Some identities on the q-Euler polynomials of higher order and q-stirling numbers by the fermionic p-adic integral on \Bbb Zp,” Russian Journal of Mathematical Physics, vol. 16, no. 4, pp. 484-491, 2009. · Zbl 1192.05011 · doi:10.1134/S1061920809040037
[5] T. Kim, J. Y. Choi, and J. Y. Sug, “Extended q-euler numbers and polynomials associated with fermionic p-adic q-integral on \Bbb Zp,” Russian Journal of Mathematical Physics, vol. 14, no. 2, pp. 160-163, 2007. · Zbl 1132.33331 · doi:10.1134/S1061920807020045
[6] T. Kim, “A note on q-Bernstein polynomials,” Russian Journal of Mathematical Physic, vol. 18, no. 4, pp. 73-82, 2011. · Zbl 1256.11018
[7] L. C. Jang, W.-J. Kim, and Y. Simsek, “A study on the p-adic integral representation on \Bbb Zp associated with Bernstein and Bernoulli polynomials,” Advances in Difference Equations, vol. 2010, Article ID 163217, 6 pages, 2010. · Zbl 1221.11058 · doi:10.1155/2010/163217
[8] L. C. Jang, K.-W. Hwang, and Y.-H. Kim, “A note on (h, q)-Genocchi polynomials and numbers of higher order,” Advances in Difference Equations, vol. 2010, Article ID 309480, 6 pages, 2010. · Zbl 1258.11031 · doi:10.1155/2010/309480
[9] M. Can, M. Cenkci, V. Kurt, and Y. Simsek, “Twisted Dedekind type sums associated with Barnes’ type multiple Frobenius-Euler l-functions,” Advanced Studies in Contemporary Mathematics, vol. 18, no. 2, pp. 135-160, 2009. · Zbl 1198.11044
[10] Y. Simsek, “Special functions related to Dedekind-type DC-sums and their applications,” Russian Journal of Mathematical Physics, vol. 17, no. 4, pp. 495-508, 2010. · Zbl 1259.11045 · doi:10.1134/S1061920810040114
[11] Y. Simsek, O. Yurekli, and V. Kurt, “On interpolation functions of the twisted generalized Frobenius-Euler numbers,” Advanced Studies in Contemporary Mathematics, vol. 15, pp. 187-194, 2007. · Zbl 1217.11115
[12] C. S. Ryoo, “A note on the weighted q-Euler numbers and polynomials,” Advanced Studies in Contemporary Mathematics, vol. 21, pp. 47-54, 2011. · Zbl 1276.11037
[13] S. H. Rim, S. J. Lee, E. J. Moon, and J. H. Jin, “On the q-Genocchi numbers and polynomials associated with Q-zeta function,” Proceedings of the Jangjeon Mathematical Society, vol. 12, no. 3, pp. 261-267, 2009. · Zbl 1213.05009
[14] C. S. Ryoo, “On the generalized Barnes type multiple q-Euler polynomials twisted by ramified roots of unity,” Proceedings of the Jangjeon Mathematical Society, vol. 13, no. 2, pp. 255-263, 2010. · Zbl 1246.11057
[15] A. Bayad, “Modular properties of elliptic Bernoulli and Euler functions,” Advanced Studies in Contemporary Mathematics, vol. 20, no. 3, pp. 389-401, 2010. · Zbl 1278.11021
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