[Octave-bug-tracker] [bug #40362] chi2cdf/gamcdf/gammainc bug

[T.J. Gaffney]

Follow-up Comment #4, bug #40362 (project octave):

To compute the incomplete gamma function, GNU Scientific Library uses
sometimes the continued fraction (which Octave uses) and sometimes a Taylor
series.  (The two methods are discussed in section 5 of
https://www.cs.purdue.edu/homes/wxg/selected_works/section_02/068.pdf)

I'm not able to follow how it makes the decision between the two, because it
also uses a number of special cases.  However, I have checked that in these
cases where Octave is failing, the series solution does converge.  By
modifying d6lgit.f, I told it to try the series solution every time that the
continued fraction fails.  This resolves the problem without adding any extra
computation time for the cases that are working already.  Although, it wastes
time in these special new cases.  So maybe a more elegant solution is needed.

Either way it comes down to:  We need to use the series computation in these
cases, but Octave currently only uses the continued fraction computation.

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