Algorithm 542: Incomplete Gamma Functions [S14]
ACM Transactions on Mathematical Software (TOMS)
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Computing the incomplete Gamma function to arbitrary precision
ICCSA'03 Proceedings of the 2003 international conference on Computational science and its applications: PartI
Algorithm 926: Incomplete Gamma Functions with Negative Arguments
ACM Transactions on Mathematical Software (TOMS)
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It is known that the recurrence relation for incomplete gamma functions {&ggr;(a + n, x)}, 0 ≤ a n = 0, 1, 2 ..., when x is positive, is unstable—more so the larger x. Nevertheless, the recursion can be used in the range 0 ≤ n ≤ x practically without error growth, and in larger ranges 0 ≤ n ≤ N with a loss of accuracy that can be controlled by suitably limiting N.