Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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ON THE SYMMETRY PROPERTIES OF THE GENERALIZED HIGHER-ORDER EULER POLYNOMIALS

  • Bayad, Abdelmejid (Departement de mathematiques, Universite d'Evry Val d'Essone) ;
  • Kim, Tae-Kyun (Division of General Education-Mathematics, Kwangwoon University) ;
  • Choi, Jong-Sung (Division of General Education-Mathematics, Kwangwoon University) ;
  • Kim, Young-Hee (Division of General Education-Mathematics, Kwangwoon University) ;
  • Lee, Byung-Je (Department of Wireless Communications Engineering, Kwangwoon University)
  • Received : 2010.10.06
  • Accepted : 2010.11.05
  • Published : 2011.01.30
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Abstract

In this paper we prove a generalized symmetry relation between the generalized Euler polynomials and the generalized higher-order (attached to Dirichlet character) Euler polynomials. Indeed, we prove a relation between the power sum polynomials and the generalized higher-order Euler polynomials..

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Acknowledgement

Supported by : Kwangwoon University

References

  1. A. Bayad, Arithmetical properties of elliptic Bernoulli and Euler numbers, to appear in the International Journal of Algebra (2010).
  2. L. C. Comtet, Advanced Combinatories, Reidel, Dordrecht, 1974.
  3. T. Kim, Symmetry p-adic invariant integral on Zp for Bernoulli and Euler polynomials, J. Difference Equ. Appl. 14(2008), 1267-1277. https://doi.org/10.1080/10236190801943220
  4. T. Kim, Symmetry identities for the twisted generalized Euler polynomials, Adv. Stud. Contemp. Math. 19(2009), 111-118.
  5. T. Kim, Some identities of symmetry for the generalized Bernoulli numbers and polynomials, arXiv, http://arxiv.org/pdf/0903.2955. (2009).
  6. T. Kim, Symmetry properties of the generalized higher-order Euler polynomials, Proc. Jangjeon Math. Soc. 13(2010), 13-16.