Affiliation:
1. US Naval Surface Weapons Center, Dahlgren, VA
Abstract
An algorithm is given for computing the incomplete gamma function ratios
P
(
a
,
x
) and
Q>
(
a
,
x
) for
a
⪈ 0,
x
⪈ 0,
a
+
x
≠ 0. Temme's uniform asymptotic expansions are used. The algorithm is robust; results accurate to 14 significant digits can be obtained. An' extensive set of coefficients for the Temme expansions is included.
An algorithm, employing third-order Schröder iteration supported by Newton-Raphson iteration, is provided for computing
x
when
a
,
P
(
a
,
x
), and
Q
(
a
,
x
) are given. Three iterations at most are required to obtain 10 significant digit accuracy for
x
.
Publisher
Association for Computing Machinery (ACM)
Subject
Applied Mathematics,Software
Cited by
60 articles.
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