Hi Raymond et al.,

Before proceeding much further, one question I'd like to clarify is
what form this documentation will take eventually.

Will it become part of the documentation for ellint_Kcomp,
ellint_Ecomp and ellipke (what one would see when typing "help
function_name" at the octave prompt)? If so, then should the
documentation effort underway take the form of patches to ellpke.m and
buildgsl_sf.sh? Working on a LaTeX based document is fine for me, but
if the goal is to eventually improve the functions' documentation,
perhaps switching to the structure described in the "Octave
Documentation Strings Tips" [1] soon should be considered. I bring
this up since I think this may impact the structure of the
documentation. For example, the current document has all forms of the
elliptic integrals defined in the GSL section whereas for online
documentation, I think something will be needed in the ellipke.m
section.

Two technical points:

I would remove the general Legendre form definitions from the
documentation. I think the important point to document is that the
definitions used by ellipke and ellint_[KE]comp are different.

ellipke accepts n x 1 arrays as you wrote, but also n x m arrays, if m
>= 2.

Kristjan

[1] 
http://www.gnu.org/software/octave/doc/interpreter/Documentation-Tips.html#Documentation-Tips


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