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Euler Numbers and Polynomials Associated with Zeta Functions

Author

Listed:
  • Taekyun Kim

Abstract

For , the Euler zeta function and the Hurwitz-type Euler zeta function are defined by , and . Thus, we note that the Euler zeta functions are entire functions in whole complex -plane, and these zeta functions have the values of the Euler numbers or the Euler polynomials at negative integers. That is, , and . We give some interesting identities between the Euler numbers and the zeta functions. Finally, we will give the new values of the Euler zeta function at positive even integers.

Suggested Citation

  • Taekyun Kim, 2008. "Euler Numbers and Polynomials Associated with Zeta Functions," Abstract and Applied Analysis, Hindawi, vol. 2008, pages 1-11, May.
    • Handle: RePEc:hin:jnlaaa:581582
    DOI: 10.1155/2008/581582
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    Citations

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    Cited by:

    1. C. S. Ryoo, 2014. "Zeros of Analytic Continued q‐Euler Polynomials and q‐Euler Zeta Function," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    2. Seog-Hoon Rim & Kyoung Ho Park & Eun Jung Moon, 2008. "On Genocchi Numbers and Polynomials," Abstract and Applied Analysis, John Wiley & Sons, vol. 2008(1).
    3. Taekyun Kim & Byungje Lee, 2009. "Some Identities of the Frobenius‐Euler Polynomials," Abstract and Applied Analysis, John Wiley & Sons, vol. 2009(1).
    4. Imju Lee & Dae San Kim, 2012. "Derivation of Identities Involving Bernoulli and Euler Numbers," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2012, pages 1-14, September.
    5. T. Kim & S. H. Lee & D. V. Dolgy & C. S. Ryoo, 2011. "A Note on the Generalized q‐Bernoulli Measures with Weight α," Abstract and Applied Analysis, John Wiley & Sons, vol. 2011(1).
    6. D. S. Kim & T. Kim & W. J. Kim & D. V. Dolgy, 2012. "A Note on Eulerian Polynomials," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    7. C. S. Ryoo, 2014. "Dynamics of the Zeros of Analytic Continued (h, q)‐Euler Polynomials," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    8. Cheon Seoung Ryoo & Hyuck In Kwon & Jihee Yoon & Yu Seon Jang, 2014. "Fourier Series of the Periodic Bernoulli and Euler Functions," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    9. Leechae Jang & Taekyun Kim, 2008. "q‐Genocchi Numbers and Polynomials Associated with Fermionic p‐Adic Invariant Integrals on ℤp," Abstract and Applied Analysis, John Wiley & Sons, vol. 2008(1).
    10. Guohui Chen & Li Chen, 2018. "Some Identities Involving the Fubini Polynomials and Euler Polynomials," Mathematics, MDPI, vol. 6(12), pages 1-6, December.
    11. Mehmet Acikgoz & Yilmaz Simsek, 2009. "On Multiple Interpolation Functions of the Nörlund‐Type q‐Euler Polynomials," Abstract and Applied Analysis, John Wiley & Sons, vol. 2009(1).
    12. D. S. Kim & D. V. Dolgy & T. Kim & S.-H. Rim, 2012. "Some Formulae for the Product of Two Bernoulli and Euler Polynomials," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).

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