×
Kim, Dae San; Kim, Taekyun; Lee, Sang-Hun; Dolgy, D. V.; Rim, Seog-Hoon

Some new identities on the Bernoulli and Euler numbers. (English) Zbl 1248.11017

Discrete Dyn. Nat. Soc. 2011, Article ID 856132, 11 p. (2011).
Summary: We give some new identities on the Bernoulli and Euler numbers by using the bosonic \(p\)-adic integral on \(\mathbb Z_p\) and reflection symmetric properties of Bernoulli and Euler polynomials.

Cited in 1 Review
Cited in 6 Documents

MSC:

11B68 Bernoulli and Euler numbers and polynomials
11S40 Zeta functions and \(L\)-functions
11S80 Other analytic theory (analogues of beta and gamma functions, \(p\)-adic integration, etc.)

Keywords:

Bernoulli numbers; Euler numbers; bosonic \(p\)-adic integral
PDF BibTeX XML Cite
\textit{D. S. Kim} et al., Discrete Dyn. Nat. Soc. 2011, Article ID 856132, 11 p. (2011; Zbl 1248.11017)
Full Text: DOI
  • logo of hbz
  • logo of WorldCat

References:

[1] T. Kim, “Symmetry p-adic invariant integral on \Bbb Zp for Bernoulli and Euler polynomials,” Journal of Difference Equations and Applications, vol. 14, no. 12, pp. 1267-1277, 2008. · Zbl 1229.11152
[2] 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
[3] 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
[4] L. Jang, “A note on Kummer congruence for the Bernoulli numbers of higher order,” Proceedings of the Jangjeon Mathematical Society, vol. 5, no. 2, pp. 141-146, 2002. · Zbl 1059.11502
[5] L. C. Jang and H. K. Pak, “Non-Archimedean integration associated with q-Bernoulli numbers,” Proceedings of the Jangjeon Mathematical Society, vol. 5, no. 2, pp. 125-129, 2002. · Zbl 1049.11020
[6] G. Kim, B. Kim, and J. Choi, “The DC algorithm for computing sums of powers of consecutive integers and Bernoulli numbers,” Advanced Studies in Contemporary Mathematics, vol. 17, no. 2, pp. 137-145, 2008. · Zbl 1172.11312
[7] 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
[8] T. Kim, “Euler numbers and polynomials associated with zeta functions,” Abstract and Applied Analysis, vol. 2008, Article ID 581582, 11 pages, 2008. · Zbl 1145.11019
[9] T. Kim, “Note on the Euler numbers and polynomials,” Advanced Studies in Contemporary Mathematics, vol. 17, no. 2, pp. 131-136, 2008. · Zbl 1171.11011
[10] T. Kim, “On explicit formulas of p-adic q-L-functions,” Kyushu Journal of Mathematics, vol. 48, no. 1, pp. 73-86, 1994. · Zbl 0817.11054
[11] T. Kim, “Symmetry of power sum polynomials and multivariate fermionic p-adic invariant integral on \Bbb Zp,” Russian Journal of Mathematical Physics, vol. 16, no. 1, pp. 93-96, 2009. · Zbl 1200.11089
[12] T. Kim, “q-Volkenborn integration,” Russian Journal of Mathematical Physics, vol. 9, no. 3, pp. 288-299, 2002. · Zbl 1092.11045
[13] T. Kim, “A note on q-Bernstein polynomials,” Russian Journal of Mathematical Physics, vol. 18, no. 2, pp. 14-50, 2011.
[14] A. Kudo, “A congruence of generalized Bernoulli number for the character of the first kind,” Advanced Studies in Contemporary Mathematics, vol. 2, pp. 1-8, 2000. · Zbl 0982.11067
[15] H. Ozden, I. N. Cangul, and Y. Simsek, “Remarks on q-Bernoulli numbers associated with Daehee numbers,” Advanced Studies in Contemporary Mathematics, vol. 18, no. 1, pp. 41-48, 2009. · Zbl 1188.05005
[16] 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
[17] 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
[18] I. Buyukyazici, “On Generalized q-Bernstein Polynomials,” Global Journal of Pure and Applied Mathematics, vol. 6, no. 3, pp. 1331-1348, 2010.
[19] Y. Simsek, “Generating functions of the twisted Bernoulli numbers and polynomials associated with their interpolation functions,” Advanced Studies in Contemporary Mathematics, vol. 16, no. 2, pp. 251-278, 2008. · Zbl 1173.11064
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.