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An extension of the Taylor series expansion by using the Bell polynomials

  • Mohammad Masjed-Jamei
  • Zahra Moalemi
  • Wolfram Koepf
  • H. M. SrivastavaEmail author
Original Paper

Abstract

By using the Bell polynomials, we introduce an extension of the Taylor series expansion and consider some of its special cases leading to new series and new identities. We also apply the extended expansion for deriving generating functions of such widely-investigated sequences of numbers as (for example) the Stirling numbers of the first and second kind.

Keywords

Bell polynomials Taylor series expansion Interpolation formulas Generating functions Stirling numbers, Lagrange, Newton and Hermite interpolations Lagrange inversion theorem Polylogarithm function (or de Jonquière’s function)  function Biorthogonality relation 

Mathematics Subject Classification

Primary 65D05 Secondary 41A05 42A15 

Notes

Acknowledgements

The work of the first-named author was supported by the Alexander von Humboldt Foundation under Grant Number: Ref. 3.4-IRN-1128637-GF-E.

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Copyright information

© Springer-Verlag Italia S.r.l., part of Springer Nature 2018

Authors and Affiliations

  • Mohammad Masjed-Jamei
    • 1
  • Zahra Moalemi
    • 1
  • Wolfram Koepf
    • 2
  • H. M. Srivastava
    • 3
    • 4
    Email author
  1. 1.Department of MathematicsK. N. Toosi University of TechnologyTehranIran
  2. 2.Department of MathematicsUniversity of KasselKasselGermany
  3. 3.Department of Mathematics and StatisticsUniversity of VictoriaVictoriaCanada
  4. 4.Department of Medical Research, China Medical University HospitalChina Medical UniversityTaichungRepublic of China

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