When to simplify complete elliptic integrals?

Richard Fateman wrote:
> It seems to me that some people might prefer elliptic functions over 
> gamma functions, so making the transformation all the time may be 
> unsatisfactory to some people.
> How to control this situation is analogous to lots of others, though.
>   
I think that's why the simplification of elliptic functions is done via
makegamma.   Well, plus the fact that that's how some other functions
were done, so I was copying that.  But after several years, I had
forgotten about it, and was adding the simplification in the elliptic
function routines themselves.

Now I'm debating whether to continue with the old scheme of using
makegamma, or moving the simplification to the elliptic functions
themselves.

I agree with Dieter that it's easier to find and understand if it's in
the elliptic functions instead of being spread around in other
functions.  But, as you say, sometimes elliptic_ec(1/2) is better than
the somewhat messy version in terms of gamma(1/4).  At least it's
documented to use makegamma to convert some elliptic_ec to gamma
functions if possible. :-)

Can't decide what to do....

Ray