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An algorithm for the evaluation of the incomplete gamma function

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Abstract

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.

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Authors and Affiliations

  1. Yale University, 51 Prospect Street, New Haven, CT, 06511, USA

    Philip Greengard & Vladimir Rokhlin

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  1. Philip Greengard
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  2. Vladimir Rokhlin
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Correspondence to Philip Greengard.

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Communicated by: Zydrunas Gimbutas

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Greengard, P., Rokhlin, V. An algorithm for the evaluation of the incomplete gamma function. Adv Comput Math 45, 23–49 (2019). https://doi.org/10.1007/s10444-018-9604-x

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  • DOI: https://doi.org/10.1007/s10444-018-9604-x

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