A New Type of Euler Polynomials and Numbers

  • M. Masjed-Jamei
  • M. R. Beyki
  • W. KoepfEmail author


By defining two specific exponential generating functions, we introduce a kind of Euler polynomials and study its basic properties in detail. As an application of the introduced polynomials, we use them in computing some new series of Taylor type that contain the associated Euler numbers \(E_n(0)\) where \(E_n(x)\) is the Euler polynomial.


Euler numbers and polynomials Appell polynomials binomial convolution exponential generating functions 

Mathematics Subject Classification

11B68 11C08 11Y35 


  1. 1.
    Tempesta, P.: Formal groups, Bernoulli-type polynomials and \(L\)-series. C. R. Math. Acad. Sci. Paris 345, 303–306 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Avram, F., Taqqu, M.S.: Noncentral limit theorems and Appell polynomials. Ann. Probab. 15, 767–775 (1987)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Jolany, H., Eizadi Alikelaye, R., Sharif Mohamad, S.: Some results on the generalization of Bernoulli, Euler and Genocchi polynomials. Acta Univ. Apulensis Math. Inform. 27, 299–306 (2011)MathSciNetzbMATHGoogle Scholar
  4. 4.
    Jolany, H., Corcino, R.B., Komatsu, T.: More properties on multi-poly-Euler polynomials. Bol. Soc. Math. Mex. 21, 149–162 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Jiu, L., Moll, V.H., Vignat, C.: Identities for generalized Euler polynomials. Integral Transforms Spec. Funct. 25, 777–789 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Ohno, Y., Sasaki, Y.: On the parity of poly-Euler numbers. RIMS Kôkyûroku Bessatsu B32, 271–278 (2012)MathSciNetzbMATHGoogle Scholar
  7. 7.
    Masjed-Jamei, M., Koepf, W.: Symbolic computation of some power-trigonometric series. J. Symb. Comput. 80, 273–284 (2017)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsK. N. Toosi University of TechnologyTehranIran
  2. 2.Department of MathematicsUniversity of KasselKasselGermany

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