Hi Mario, you wrote in part:
> I think Maxima has no implementations of the incomplete
> gamma and beta functions, am I right?
So far as I know there are no numerical functions for these two.
I think there are some simplification rules for incomplete
gamma, but nothing for incomplete beta so far as I know.
You might consider translating an existing Fortran
implementation to Lisp, using f2cl which you can find
in cvs at http://clocc.sourceforge.net.
Just now I tried translating dbetai.f and dgami.f (plus
dependencies in each case) from http://netlib.org/slatec/fnlib
-- f2cl prints a lot of warnings, which appear to be entirely
about floating point contagion and an undefined function named
xermsg. Not to worry, then. (load "dbetai.lisp") and
(load "dgami.lisp") succeed, and dbetai and dgami appear to
function as advertised, except that (dgami a x) fails with
"NIL is not a NUMBER" if a > x. Rats! Dunno what that's about.
There are many numerical functions in the src/numerical/slatec
directory of Maxima, but not all of fnlib -- maybe at some
point we can consider bringing in other SLATEC functions.
> And the Riemann-zeta lacks some values, as well:
There is a function bfzeta in the bffac package (somewhere
in the share directory) -- load (bffac)$ should load it.
bfzeta returns a bigfloat (not an ordinary float).
I don't know anything about bfzeta, such as how reliable it is.
There doesn't appear to be a zeta function at netlib.
Hope this helps,
Robert Dodier
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