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Some Relationships between the Analogs of Euler Numbers and Polynomials

Abstract

We construct new twisted Euler polynomials and numbers. We also study the generating functions of the twisted Euler numbers and polynomials associated with their interpolation functions. Next we construct twisted Euler zeta function, twisted Hurwitz zeta function, twisted Dirichlet-Euler numbers and twisted Euler polynomials at non-positive integers, respectively. Furthermore, we find distribution relations of generalized twisted Euler numbers and polynomials. By numerical experiments, we demonstrate a remarkably regular structure of the complex roots of the twisted-Euler polynomials. Finally, we give a table for the solutions of the twisted-Euler polynomials.

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Correspondence to CS Ryoo.

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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.

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Ryoo, C., Kim, T. & Jang, LC. Some Relationships between the Analogs of Euler Numbers and Polynomials. J Inequal Appl 2007, 086052 (2007). https://doi.org/10.1155/2007/86052

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Keywords

  • Numerical Experiment
  • Zeta Function
  • Distribution Relation
  • Interpolation Function
  • Regular Structure
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