An algorithm for the evaluation of the incomplete gamma function

  • Philip Greengard
  • Vladimir Rokhlin


We introduce an algorithm for the evaluation of the Incomplete Gamma Function, P(m, x), for all m, x > 0. For small m, a classical recursive scheme is used to evaluate P(m, x), whereas for large m a newly derived asymptotic expansion is used. The number of operations required for evaluation is O(1) for all x and m. Nearly full double and extended precision accuracies are achieved in their respective environments. The performance of the scheme is illustrated via several numerical examples.


Incomplete gamma function Special functions Numerical evaluation 

Mathematics Subject Classification (2010)



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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Yale UniversityNew HavenUSA

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