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- Log ----------------------------------------------------------------- commit 08d254374188f97026d114451bba5d839dbdad11 Author: Raymond Toy toy.raymond@gmail.com Date: Mon Mar 28 22:54:32 2011 -0400

Make INCOMPLETE-GAMMA-TAIL more accurate.

o Use the new continued fraction for the incomplete-gamma when the argument z is close enough to the negative real axis.

diff --git a/qd-gamma.lisp b/qd-gamma.lisp index e020a91..7048b80 100644 --- a/qd-gamma.lisp +++ b/qd-gamma.lisp @@ -372,8 +372,15 @@ (if (and (> (abs z) (abs (- a 1))) (not (minusp (realpart z)))) (cf-incomplete-gamma-tail a z) - (- (gamma a) (incomplete-gamma a z))) - (cf-incomplete-gamma-tail a z)))) + (- (gamma a) (cf-incomplete-gamma a z))) + ;; If the argument is close enough to the negative real axis, + ;; the continued fraction for the tail is not very accurate. + ;; Use the incomplete gamma function to evaluate in this + ;; region. (Arbitrarily selected the region to be a sector. + ;; But what is the correct size of this sector?) + (if (<= (phase z) 3.1) + (cf-incomplete-gamma-tail a z) + (- (gamma a) (cf-incomplete-gamma a z))))))

(defun incomplete-gamma (a z) "Incomplete gamma function defined by:

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Summary of changes: qd-gamma.lisp | 11 +++++++++-- 1 files changed, 9 insertions(+), 2 deletions(-)

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