[with patch, positive review] missing elliptic integrals in special.py

[wdj]

The following problem was reported by Dustin Vaselaar to sage-support:

Hello, I am looking to use a complete elliptic integral of the first kind in sage, however I'm not sure if this has been implemented. The link http://www.sagemath.org/doc/html/ref/module-sage.functions.special.html mentions a function "elliptic_kc", but it doesn't seem to be implemented in sage version 3.0, judging from the result of this command:

sage: elliptic_kc?
Object `elliptic_kc` not found.

Any insights on using a a complete elliptic integral of the first kind in sage?

[wdj]

Clearly this is a problem with "documentation" but I filed it under "calculus" since that seemed closer. It is a matter of adding a wrapper to Maxima's function elliptic_kc.

sage: RR(maxima.eval("elliptic_kc (0.5)"))
1.85407467730137

I'll submit a patch soon.

[wdj]

Thinking about this problem more, I think it is my fault. In any case, a patch is attached. It is based on 3.0 and passes sage -t but my (old) machine froze (as it very often does) during the sage -testall. No errors were reported before the freeze.

[AlexGhitza]

Looks good.

[mabshoff]

Merged in Sage 3.0.1.alpha0