Skip to main content

A Note on the-Genocchi Numbers and Polynomials

Abstract

We discuss new concept of the-extension of Genocchi numbers and give some relations between-Genocchi polynomials and-Euler numbers.

[12345678910111213141516]

References

  1. 1.

    Cenkci M, Can M, Kurt V: -extensions of Genocchi numbers. Journal of the Korean Mathematical Society 2006,43(1):183–198.

    MathSciNet  Article  MATH  Google Scholar 

  2. 2.

    Cenkci M, Can M: Some results on-analogue of the Lerch zeta function. Advanced Studies in Contemporary Mathematics 2006,12(2):213–223.

    MathSciNet  MATH  Google Scholar 

  3. 3.

    Howard FT: Applications of a recurrence for the Bernoulli numbers. Journal of Number Theory 1995,52(1):157–172. 10.1006/jnth.1995.1062

    MathSciNet  Article  MATH  Google Scholar 

  4. 4.

    Kim T: A note on-Volkenborn integration. Proceedings of the Jangjeon Mathematical Society 2005,8(1):13–17.

    MathSciNet  MATH  Google Scholar 

  5. 5.

    Kim T: -Volkenborn integration. Russian Journal of Mathematical Physics 2002,9(3):288–299.

    MathSciNet  MATH  Google Scholar 

  6. 6.

    Kim T: A note on-adic invariant integral in the rings of-adic integers. Advanced Studies in Contemporary Mathematics 2006,13(1):95–99.

    MathSciNet  MATH  Google Scholar 

  7. 7.

    Kim T, Jang L-C, Pak HK: A note on-Euler and Genocchi numbers. Proceedings of the Japan Academy, Series A 2001,77(8):139–141. 10.3792/pjaa.77.139

    MathSciNet  Article  MATH  Google Scholar 

  8. 8.

    Kim T: A note on some formulas for the-Euler numbers and polynomials. Proceedings of the Jangjeon Mathematical Society 2006, 9: 227–232.

    MathSciNet  MATH  Google Scholar 

  9. 9.

    Kim T, Choi JY, Sug JY: Extended-Euler numbers and polynomials associated with fermionic-adic-integrals on. Russian Journal of Mathematical Physics 2007, 14: 160–163. 10.1134/S1061920807020045

    MathSciNet  Article  MATH  Google Scholar 

  10. 10.

    Kim T: The modified-Euler numbers and polynomials. 2006.http://arxiv.org/abs/math/0702523

    Google Scholar 

  11. 11.

    Kim T: An invariant-adic-integral on. to appear in Applied Mathematics Letters to appear in Applied Mathematics Letters

  12. 12.

    Srivastava HM, Kim T, Simsek Y: -Bernoulli numbers and polynomials associated with multiple-zeta functions and basic-series. Russian Journal of Mathematical Physics 2005,12(2):241–268.

    MathSciNet  MATH  Google Scholar 

  13. 13.

    Schork M: Ward's "calculus of sequences",-calculus and the limit. Advanced Studies in Contemporary Mathematics 2006,13(2):131–141.

    MathSciNet  MATH  Google Scholar 

  14. 14.

    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

    MathSciNet  Article  MATH  Google Scholar 

  15. 15.

    Kim T: Non-Archimedean-integrals associated with multiple Changhee-Bernoulli polynomials. Russian Journal of Mathematical Physics 2003,10(1):91–98.

    MathSciNet  MATH  Google Scholar 

  16. 16.

    Kim T: On Euler-Barnes multiple zeta functions. Russian Journal of Mathematical Physics 2003,10(3):261–267.

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to Taekyun Kim.

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.

Reprints and Permissions

About this article

Cite this article

Kim, T. A Note on the-Genocchi Numbers and Polynomials. J Inequal Appl 2007, 071452 (2007). https://doi.org/10.1155/2007/71452

Download citation

Keywords

  • Euler Number
  • Genocchi Polynomial
  • Genocchi Number