A note on the recursive calculation of incomplete gamma functions

Authors
Gautschi, W
Citation
W. Gautschi, A note on the recursive calculation of incomplete gamma functions, ACM T MATH, 25(1), 1999, pp. 101-107
Citations number
8
Categorie Soggetti
Computer Science & Engineering
Journal title
ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE
ISSN journal
00983500 → ACNP
Volume
25
Issue
1
Year of publication
1999
Pages
101 - 107
Database
ISI
SICI code
0098-3500(199903)25:1<101:ANOTRC>2.0.ZU;2-B
Abstract
It is known that the recurrence relation for incomplete gamma functions {ga mma(a + n, x)}, 0 less than or equal to a < 1, n = 0,1,2,...,when x is posi tive, is unstable-more so the larger x. Nevertheless, the recursion can be used in the range 0 less than or equal to n less than or equal to x practic ally without error growth, and in larger ranges 0 less than or equal to n l ess than or equal to N with a loss of accuracy that can be controlled by su itably limiting N.