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International Conference on Mathematical Aspects of Computer and Information Sciences

MACIS 2017: Mathematical Aspects of Computer and Information Sciences pp 275–279Cite as

Stirling Numbers, Lambert W and the Gamma Function

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10693))

Abstract

Stirling’s asymptotic expansion for the Gamma function can be derived from an expansion of the Lambert W function about one of its branch points. Although the series expansions around this branch point have been known for some time, the coefficients in the series were only known as solutions of nonlinear recurrence relations. Here we show that the coefficients can be expressed using associated Stirling numbers.

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References

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Author information

Authors and Affiliations

  1. Department of Applied Mathematics, The University of Western Ontario, London, ON, N6G 2B3, Canada

    David J. Jeffrey & Nick Murdoch

Authors
  1. David J. Jeffrey
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  2. Nick Murdoch
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Corresponding author

Correspondence to David J. Jeffrey .

Editor information

Editors and Affiliations

  1. University of Paderborn, Paderborn, Germany

    Johannes Blömer

  2. Wilfrid Laurier University, Waterloo, Ontario, Canada

    Ilias S. Kotsireas

  3. Johannes Kepler University Linz, Linz, Austria

    Temur Kutsia

  4. SBA Research, Vienna, Austria

    Dimitris E. Simos

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Jeffrey, D.J., Murdoch, N. (2017). Stirling Numbers, Lambert W and the Gamma Function. In: Blömer, J., Kotsireas, I., Kutsia, T., Simos, D. (eds) Mathematical Aspects of Computer and Information Sciences. MACIS 2017. Lecture Notes in Computer Science(), vol 10693. Springer, Cham. https://doi.org/10.1007/978-3-319-72453-9_21

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  • DOI: https://doi.org/10.1007/978-3-319-72453-9_21

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-72452-2

  • Online ISBN: 978-3-319-72453-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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