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

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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.

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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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Authors and Affiliations

  1. Department of Mathematics, K. N. Toosi University of Technology, P. O. Box 1618, Tehran, 16315-1618, Iran

    Mohammad Masjed-Jamei & Zahra Moalemi

  2. Department of Mathematics, University of Kassel, Heinrich-Plett-Strasse 40, 34132, Kassel, Germany

    Wolfram Koepf

  3. Department of Mathematics and Statistics, University of Victoria, Victoria, BC, V8W 3R4, Canada

    H. M. Srivastava

  4. Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, 40402, Taiwan, Republic of China

    H. M. Srivastava

Authors
  1. Mohammad Masjed-Jamei
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  2. Zahra Moalemi
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  3. Wolfram Koepf
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  4. H. M. Srivastava
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Corresponding author

Correspondence to H. M. Srivastava.

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Masjed-Jamei, M., Moalemi, Z., Koepf, W. et al. An extension of the Taylor series expansion by using the Bell polynomials. RACSAM 113, 1445–1461 (2019). https://doi.org/10.1007/s13398-018-0558-0

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  • DOI: https://doi.org/10.1007/s13398-018-0558-0

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