Dieter,
Is any of this going to make it into version 5.17?
Rich
----- Original Message -----
From: "Dieter Kaiser" <drdieterkaiser at web.de>
To: <maxima at math.utexas.edu>
Sent: Friday, December 19, 2008 6:49 PM
Subject: Improving the Incomplete Gamma function
I have committed changes for the numerical evaluation of the Incomplete Gamma
function. With these changes the example on this mailing list to calculate the
Fresnel integrals with the help of the Erf function no longer fails. The
gamma_incomplete function now gives the results within an expected accuracy.
I have studied some more papers about the numerical evaluation of the Incomplete
Gamma function. It is a known problem to get correct result for increasing
parameter a and argument z for realpart(z)<0. The series expansion as well as
the expansion in continued fractions converge mathematically but not in praxis.
I had no problems with the testsuite. But I have tested the share_testsuite too.
There is one problem which is related to the gamma_incomplete and the
gamma_incomplete_regualarized function:
Running tests in rtest_distrib:
********************** Problem 15 ***************
Input:
cdf_noncentral_chi2(13.1, 2, 8)
Result:
Caused an error break: rtest_distrib
The error is due to an overflow in the numerical calculation within the
gamma_incomplete_regularized function.
In principle the overflow can be avoided for this case. The
gamma_incomplete_regularized function is calculated as
gammma_incomplete_regularized(a,z) = gamma_incomplete(a,z)/gamma(a)
For the above values the series expansion is used. But the sum of the expansion
gives a result in terms of the Regularized Incomplete function. So in this case
we could extend the domain of the function when we avoid the multiplication and
division with the Gamma function.
I will have a look at this problem.
Dieter Kaiser
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