Fast and accurate evaluation of a generalized incomplete gamma function

Abstract : 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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https://hal.archives-ouvertes.fr/hal-01329669
Contributor : Lionel Moisan <>
Submitted on : Thursday, June 9, 2016 - 2:53:15 PM
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Rémy Abergel, Lionel Moisan. Fast and accurate evaluation of a generalized incomplete gamma function. 2016. ⟨hal-01329669⟩

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