- Research Article
- Open access
- Published:
A note on Euler number and polynomials
Journal of Inequalities and Applications volume 2006, Article number: 34602 (2006)
Abstract
We investigate some properties of non-Archimedean integration which is defined by Kim. By using our results in this paper, we can give an answer to the problem which is introduced by I.-C. Huang and S.-Y. Huang in 1999.
References
Carlitz L: -Bernoulli numbers and polynomials. Duke Mathematical Journal 1948, 15: 987–1000. 10.1215/S0012-7094-48-01588-9
Huang I-C, Huang S-Y: Bernoulli numbers and polynomials via residues. Journal of Number Theory 1999,76(2):178–193. 10.1006/jnth.1998.2364
Kim T: On a-analogue of the-adic log gamma functions and related integrals. Journal of Number Theory 1999,76(2):320–329. 10.1006/jnth.1999.2373
Kim T: -Volkenborn integration. Russian Journal of Mathematical Physics 2002,9(3):288–298.
Kim T: An invariant-adic integral associated with Daehee numbers. Integral Transforms and Special Functions 2002,13(1):65–69. 10.1080/10652460212889
Kim T: On-adic--functions and sums of powers. Discrete Mathematics 2002,252(1–3):179–187.
Kim T: Non-Archimedean-integrals associated with multiple Changhee-Bernoulli polynomials. Russian Journal of Mathematical Physics 2003,10(1):91–98.
Kim T: On Euler-Barnes' multiple zeta functions. Russian Journal of Mathematical Physics 2003,10(3):261–267.
Kim T: -adic-integrals associated with the Changhee-Barnes'-Bernoulli polynomials. Integral Transforms and Special Functions 2004,15(5):415–420. 10.1080/10652460410001672960
Kim T: Analytic continuation of multiple-zeta functions and their values at negative integers. Russian Journal of Mathematical Physics 2004,11(1):71–76.
Kim T, Rim SH: On Changhee-Barnes'-Euler numbers and polynomials. Advanced Studies in Contemporary Mathematics 2004,9(2):81–86.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License ( https://creativecommons.org/licenses/by/2.0 ), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
About this article
Cite this article
Jang, LC., Kim, SD., Park, DW. et al. A note on Euler number and polynomials. J Inequal Appl 2006, 34602 (2006). https://doi.org/10.1155/JIA/2006/34602
Received:
Accepted:
Published:
DOI: https://doi.org/10.1155/JIA/2006/34602