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A note on Euler number and polynomials

  • Lee-Chae Jang
  • Seoung-Dong Kim
  • Dal-Won Park
  • Young-Soon Ro
Open Access
Research Article

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.

Keywords

Euler Number 
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References

  1. 1.
    Carlitz L: -Bernoulli numbers and polynomials. Duke Mathematical Journal 1948, 15: 987–1000. 10.1215/S0012-7094-48-01588-9MATHMathSciNetCrossRefGoogle Scholar
  2. 2.
    Huang I-C, Huang S-Y: Bernoulli numbers and polynomials via residues. Journal of Number Theory 1999,76(2):178–193. 10.1006/jnth.1998.2364MATHMathSciNetCrossRefGoogle Scholar
  3. 3.
    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.1999.2373MATHMathSciNetCrossRefGoogle Scholar
  4. 4.
    Kim T: -Volkenborn integration. Russian Journal of Mathematical Physics 2002,9(3):288–298.MATHMathSciNetGoogle Scholar
  5. 5.
    Kim T: An invariant-adic integral associated with Daehee numbers. Integral Transforms and Special Functions 2002,13(1):65–69. 10.1080/10652460212889MATHMathSciNetCrossRefGoogle Scholar
  6. 6.
    Kim T: On-adic--functions and sums of powers. Discrete Mathematics 2002,252(1–3):179–187.MATHMathSciNetCrossRefGoogle Scholar
  7. 7.
    Kim T: Non-Archimedean-integrals associated with multiple Changhee-Bernoulli polynomials. Russian Journal of Mathematical Physics 2003,10(1):91–98.MATHMathSciNetGoogle Scholar
  8. 8.
    Kim T: On Euler-Barnes' multiple zeta functions. Russian Journal of Mathematical Physics 2003,10(3):261–267.MATHMathSciNetGoogle Scholar
  9. 9.
    Kim T: -adic-integrals associated with the Changhee-Barnes'-Bernoulli polynomials. Integral Transforms and Special Functions 2004,15(5):415–420. 10.1080/10652460410001672960MATHMathSciNetCrossRefGoogle Scholar
  10. 10.
    Kim T: Analytic continuation of multiple-zeta functions and their values at negative integers. Russian Journal of Mathematical Physics 2004,11(1):71–76.MATHMathSciNetGoogle Scholar
  11. 11.
    Kim T, Rim SH: On Changhee-Barnes'-Euler numbers and polynomials. Advanced Studies in Contemporary Mathematics 2004,9(2):81–86.MATHMathSciNetGoogle Scholar

Copyright information

© Jang et al. 2006

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Authors and Affiliations

  • Lee-Chae Jang
    • 1
  • Seoung-Dong Kim
    • 2
  • Dal-Won Park
    • 2
  • Young-Soon Ro
    • 2
  1. 1.Department of Mathematics and Computer ScienceKonKuk UniversityChungjuKorea
  2. 2.Department of Mathematics EducationKongju National UniversityKongjuKorea

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