On Mon, Feb 19, 2024 at 11:40:13PM -0800, Emmanuel Charpentier wrote: > > Indeed. That’s probably an oversight : > sage: elliptic_kc(x).limit(x=0) 1/2*pi sage: elliptic_ec(x).limit(x=0) > limit(elliptic_ec(x), x, 0) >
this looks like a maxima bug:
(%i17) elliptic_ec(0);
%pi
(%o17) ---
2
(%i18) limit(elliptic_ec(x),x,0);
(%o18) limit elliptic_ec(x)
x -> 0
(%i19) elliptic_kc(0);
%pi
(%o19) ---
2
(%i20) limit(elliptic_kc(x),x,0);
%pi
(%o20) ---
2
No idea why limit(elliptic_ec(x),x,0) is a problem for Maxima.
> Curioisly :
> sage: elliptic_ec(0) 1/2*pi
>
> FWIW :
> sage: D(r)._mathematica_().Limit(mathematica.Rule(r, 0)) -1/8
>
> HTH,
>
> Le lundi 19 février 2024 à 21:25:51 UTC+1, Mark “Essa King” Sukaiti a
> écrit :
>
> > D(r)=-1/2*((3*r^2 - 1)*elliptic_ec((4*r/(r^2 + 2*r + 1)))^2 + (r^2 - 2*r +
> > 1)*elliptic_ec((4*r/(r^2 + 2*r + 1)))*elliptic_kc((4*r/(r^2 + 2*r +
> > 1))))/(pi^2*r^8 - 2*pi^2*r^7 - pi^2*r^6 + 4*pi^2*r^5 - pi^2*r^4 -
> > 2*pi^2*r^3 + pi^2*r^2)
> >
> > D(r).limit(r=0)
> >
> > The limit should be -0.125 (or -1/8) but it seems maxima doesnt know the
> > limit of elliptic_ec(x) for x->0
> > [image: 2024-02-20_00-22.png]
> > Sympy also fails giving -5/8.
> >
> > The other algorithms cant evaluate it either.
> >
>
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