zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Derivation of identities involving Bernoulli and Euler numbers. (English) Zbl 1258.11042
Summary: We derive some new and interesting identities involving Bernoulli and Euler numbers by using some polynomial identities and $p$-adic integrals on $\Bbb Z_p$.

MSC:
11B68Bernoulli and Euler numbers and polynomials
11S80Other analytic theory of local fields
WorldCat.org
Full Text: DOI
References:
[1] 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
[2] D. Ding and J. Yang, “Some identities related to the Apostol-Euler and Apostol-Bernoulli polynomials,” Advanced Studies in Contemporary Mathematics, vol. 20, no. 1, pp. 7-21, 2010. · Zbl 1192.05001
[3] 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
[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] D. S. Kim, T. Kim, D. V. Dolgy, J. Choi, and Y. H. Kim, “Some identities on Bernoulli and Euler numbers,” Discrete Dynamics in Nature and Society, vol. 2012, Article ID 486158, 12 pages, 2012. · doi:10.1155/2012/486158
[7] D. S. Kim, T. Kim, S.-H. Lee, D. V. Dolgy, and S.-H. Rim, “Some new identities on the Bernoulli and Euler numbers,” Discrete Dynamics in Nature and Society, vol. 2011, Article ID 856132, 11 pages, 2011. · Zbl 1248.11017 · doi:10.1155/2011/856132
[8] D. S. Kim, A. Bayad, T. Kim, and S.-H. Rim, “Identities on the Bernoulli and Euler numbers and polynomials,” Ars Combinatoria. In press.
[9] 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 · doi:10.1155/2008/581582 · eudml:54483
[10] 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
[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 · doi:10.1134/S1061920809010063
[12] 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 · doi:10.1080/10236190801943220
[13] T. Kim, “q-Volkenborn integration,” Russian Journal of Mathematical Physics, vol. 9, no. 3, pp. 288-299, 2002. · Zbl 1092.11045
[14] T. Kim, “A note on q-Bernstein polynomials,” Russian Journal of Mathematical Physics, vol. 18, no. 1, pp. 73-82, 2011. · Zbl 1256.11018 · doi:10.1134/S1061920811010080
[15] 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
[16] Q.-M. Luo and F. Qi, “Relationships between generalized Bernoulli numbers and polynomials and generalized Euler numbers and polynomials,” Advanced Studies in Contemporary Mathematics, vol. 7, no. 1, pp. 11-18, 2003. · Zbl 1042.11012
[17] Q.-M. Luo, “Some recursion formulae and relations for Bernoulli numbers and Euler numbers of higher order,” Advanced Studies in Contemporary Mathematics, vol. 10, no. 1, pp. 63-70, 2005. · Zbl 1072.11019
[18] 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
[19] Y.-H. Kim and K.-W. Hwang, “Symmetry of power sum and twisted Bernoulli polynomials,” Advanced Studies in Contemporary Mathematics, vol. 18, no. 2, pp. 127-133, 2009. · Zbl 1218.11023
[20] S.-H. Rim, J.-H. Jin, E.-J. Moon, and S.-J. Lee, “Some identities on the q-Genocchi polynomials of higher-order and q-Stirling numbers by the fermionic p-adic integral on \Bbb Zp,” International Journal of Mathematics and Mathematical Sciences, vol. 2010, Article ID 860280, 14 pages, 2010. · Zbl 1208.11031 · doi:10.1155/2010/860280
[21] 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
[22] C. S. Ryoo, “Some relations between twisted q-Euler numbers and Bernstein polynomials,” Advanced Studies in Contemporary Mathematics, vol. 21, no. 2, pp. 217-223, 2011. · Zbl 1266.11040
[23] 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