Complete Elliptic Integrals

[trophime christophe <trophime at labs dot polycnrs-gre dot fr>]

I have a few basic questions about complete elliptic integrals :

1. E(1) should return 1, right?
result = gsl_sf_ellint_Ecomp_impl(m(r1,z11), GSL_PREC_DOUBLE, &E)
returns :
E.val = 0 and  result == GSL_EDOM

2.Looking in the source I have noticed on line 246
(gsl_sf_ellint_RJ_impl) :
if(x < 0.0 || y < 0.0 || y < 0.0) {
Should I read z instead of the second y??

3.What are gsl_sf_ellint_Dcomp_impl? I can't find this notation anywhere
?

and  a very "stupid" question

1. I want to compute complete elliptic integrals of the third kind.
I guess I can use the incomplete version with phi=Pi/2:

gsl_sf_ellint_P_impl(M_PI_2, m(r,z), beta0(r), GSL_PREC_DOUBLE, &P0)

Is the result as accurate as for any phi != Pi/2?
why not providing a complete version of the third kind integrals?

Thanks for you answer