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Kim, D. S.; Kim, T.; Choi, J.; Kim, Y. H.

Identities involving \(q\)-Bernoulli and \(q\)-Euler numbers. (English) Zbl 1242.11016

Abstr. Appl. Anal. 2012, Article ID 674210, 10 p. (2012).
Summary: We give some identities on the \(q\)-Bernoulli and \(q\)-Euler numbers by using \(p\)-adic integral equations on \(\mathbb Z_p\).

Cited in 3 Documents

MSC:

11B68 Bernoulli and Euler numbers and polynomials
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References:

[1] A. Bayad and T. Kim, “Identities involving values of Bernstein, q-Bernoulli, and q-Euler polynomials,” Russian Journal of Mathematical Physics, vol. 18, no. 2, pp. 133-143, 2011. · Zbl 1256.11013 · doi:10.1134/S1061920811020014
[2] 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
[3] A. Bayad, T. Kim, B. Lee, and S.-H. Rim, “Some identities on Bernstein polynomials associated with q-Euler polynomials,” Abstract and Applied Analysis, vol. 2011, Article ID 294715, 10 pages, 2011. · Zbl 1234.11024 · doi:10.1155/2011/294715
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[6] 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
[7] T. Kim, “An analogue of Bernoulli numbers and their congruences,” Reports of the Faculty of Science and Engineering. Saga University. Mathematics, vol. 22, no. 2, pp. 21-26, 1994. · Zbl 0802.11007
[8] T. Kim, “New approach to q-Euler polynomials of higher order,” Russian Journal of Mathematical Physics, vol. 17, no. 2, pp. 218-225, 2010. · Zbl 1259.11030 · doi:10.1134/S1061920810020068
[9] Y.-H. Kim, K.-W. Hwang, and T. Kim, “Interpolation functions of the q-Genocchi and the q-Euler polynomials of higher order,” Journal of Computational Analysis and Applications, vol. 12, no. 1-B, pp. 228-238, 2010. · Zbl 1209.11101
[10] H. Ozden and Y. Simsek, “A new extension of q-Euler numbers and polynomials related to their interpolation functions,” Applied Mathematics Letters, vol. 21, no. 9, pp. 934-939, 2008. · Zbl 1152.11009 · doi:10.1016/j.aml.2007.10.005
[11] H. Ozden, I. N. Cangul, and Y. Simsek, “Multivariate interpolation functions of higher-order q-Euler numbers and their applications,” Abstract and Applied Analysis, vol. 2008, Article ID 390857, 16 pages, 2008. · Zbl 1140.11313 · doi:10.1155/2008/390857
[12] K.-H. Park, Y.-H. Kim, and T. Kim, “A note on the generalized q-Euler numbers (2),” Journal of Computational Analysis and Applications, vol. 12, no. 3, pp. 630-636, 2010. · Zbl 1206.11026
[13] C. S. Ryoo, “Some identities of the twisted q-Euler numbers and polynomials associated with q-Bernstein polynomials,” Proceedings of the Jangjeon Mathematical Society, vol. 14, no. 2, pp. 239-248, 2011. · Zbl 1255.11005
[14] Y. Simsek, “On p-adic twisted p-L-functions related to generalized twisted Bernoulli numbers,” Russian Journal of Mathematical Physics, vol. 13, no. 3, pp. 340-348, 2006. · Zbl 1163.11312 · doi:10.1134/S1061920806030095
[15] T. Kim, “A note on q-Volkenborn integration,” Proceedings of the Jangjeon Mathematical Society, vol. 8, no. 1, pp. 13-17, 2005. · Zbl 1174.11408
[16] T. Kim, “q-Euler numbers and polynomials associated with p-adic q-integrals,” Journal of Nonlinear Mathematical Physics, vol. 14, no. 1, pp. 15-27, 2007. · Zbl 1158.11009 · doi:10.2991/jnmp.2007.14.1.3
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