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Pré-Publication, Document De Travail Année : 2016

Fast and accurate evaluation of a generalized incomplete gamma function

Rémy Abergel
Lionel Moisan

Résumé

We propose a computational procedure to evaluate the generalized incomplete gamma function ∫xy sp-1 e-μs ds, for 0 ≤ x < y ≤ +∞, a real number μ ≠ 0 and a positive integer p. Our approach consists in selecting, according to the value of the parameters x, y, μ, p, the fastest and most accurate estimate among series expansions, continued fractions, recursive integration by parts, or, when x ≈ y, a first order trapezoidal rule. We show that the accuracy reached by our algorithm is nearly optimal for a large range of parameters.
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Dates et versions

hal-01329669 , version 1 (09-06-2016)
hal-01329669 , version 2 (07-11-2019)

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  • HAL Id : hal-01329669 , version 1

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Rémy Abergel, Lionel Moisan. Fast and accurate evaluation of a generalized incomplete gamma function. 2016. ⟨hal-01329669v1⟩
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