betainc and other special functions in Octave

[Rik]

Is there a special functions Summer of Code project this year?  I thought I
saw some e-mails on the list about that.

I'd like to point out bug #51157 (https://savannah.gnu.org/bugs/?51157)
where the betainc calculations are inaccurate for some values.  I did some
tracing and it comes down to the Fortran routines from Slatec that are
used.  They were last updated in 1992, and apparently are not accurate out
to the 15th or 16th digit of precision.

As a quick test, I wrote a C program that uses the GNU Scientific Library
to calculate betainc and it does get the more precise answer.  The GSL
might be a way to quickly get access to other high quality special function
code.

Just a thought,
Rik