[Maxima] Elliptic integrals take 2
raymond.toy at stericsson.com
Thu Mar 12 16:30:35 CDT 2009
I've uploaded a newer version of elliptic integrals. Look for
Use load(ellint) to load up everything. ellintreduce is still the main
entry point, and it's called as before.
What's new? Quite a few bugs were fixed and more integrals of the
second kind are handled, and integrals of the third kind that reduce to
integrals of the first and second kind are handled. Integrals of the
third kind are left in integral form. The reduction of general elliptic
integrals to integrals of the first, second, and third kinds is done,
but it might be buggy.
All of the integrals in A&S 17.4.41-17.4.52 appear to work. The results
might differ from what's given there, but the derivatives appear to match.
However, the current code also makes a mess of the elliptic integral
integrate((t-1)^2/(t^3-1)^(3/2), t). This is an elliptic integral of
the second kind that ought to reduce to integrals of the first and
second kind, but it doesn't. Oh well. More work needed.
Richard Fateman has provided some code for recognizing if a from is an
elliptic integral. I haven't done that yet, but I'll try to add that soon.
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