Stirling Numbers, Lambert W and the Gamma Function

  • David J. JeffreyEmail author
  • Nick Murdoch
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10693)


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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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Department of Applied MathematicsThe University of Western OntarioLondonCanada

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