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1 MAP5 - MAP5 - Mathématiques Appliquées à Paris 5

Abstract : We propose a computational procedure to evaluate the generalized incompletegamma function ∫xy sp-1 e-μs ds, for0 ≤ x < y ≤ +∞, a real number μ ≠ 0 and a positive integer p. Our approachconsists in selecting, according to the value of the parameters x, y, μ, p, thefastest and most accurate estimate among series expansions, continued fractions,recursive integration by parts, or, when x ≈ y, a first order trapezoidalrule. We show that the accuracy reached by our algorithm is nearly optimal for alarge range of parameters.

Keywords : incomplete gamma function continued fraction floating-point arithmetic





Author: Rémy Abergel - Lionel Moisan -

Source: https://hal.archives-ouvertes.fr/



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