       Re: Integrate Bug

• To: mathgroup at smc.vnet.net
• Subject: [mg100593] Re: Integrate Bug
• From: Valeri Astanoff <astanoff at gmail.com>
• Date: Tue, 9 Jun 2009 03:52:47 -0400 (EDT)
• References: <gv2jh5\$97b\$1@smc.vnet.net> <h0btr4\$8ju\$1@smc.vnet.net>

```On 8 juin, 12:17, Valeri Astanoff <astan... at gmail.com> wrote:
> On 5 juin, 22:05, Valeri Astanoff <astan... at gmail.com> wrote:
>
>
>
>
>
> > On 21 mai, 05:58, Ney Lemke <ney.nle... at gmail.com> wrote:
>
> > > I am trying to calculate this integral that should be positive.But th=
e
> > > answer is 0.
>
> > > In: Integrate[(1)/(z^2 + b^2 + a^2 - 2 z b Sin[\[Theta]] -
> > >     2 a b Cos[\[Theta]])^(1/2), {\[Theta], 0, 2 \[Pi]},
> > >  Assumptions -> {a > 0, b > 0, z > 0}]
>
> > > Out:0
>
> > > Anybody have notice a situation like that?
>
> > > My platform is MacOSX 10.4 and Mathematica 7.
>
> > > Best wishes,
>
> > Further to my previous post, seems that one single formula suffices :
>
> > F[a_, b_, z_] :=
> >  (4 Sqrt[a^2 + b^2 + z^2 + 2 b Sqrt[a^2 + z^2]]*
> >  Abs[Im[EllipticK[(a^4 + b^4 + 6 b^2 z^2 + z^4 +
> >  4 b^3 Sqrt[a^2 + z^2] + 4 b z^2 Sqrt[a^2 + z^2] +
> >  2 a^2 (3 b^2 + z^2 + 2 b Sqrt[a^2 + z^2]))/
> >  (a^2 - b^2 + z^2)^2]]])/Abs[a^2 - b^2 + z^2]
>
> > --
> > V.Astanoff
>
> 2009/6/6 Andreas Dieckmann <adieck... at aol.com>
>
> Hi,
>
> your expression with the complex EllipticK for the integral can be
> further simplified to:
>
> (4/Sqrt[a^2 + b^2 + z^2 + 2*b*Sqrt[a^2 + z^2]]) EllipticK[(4*b*
>      Sqrt[a^2 + z^2])/(a^2 + b^2 + z^2 + 2*b*Sqrt[a^2 + z^2])]
>
> Greetings
>
> Andreas- Masquer le texte des messages pr=E9c=E9dents -
>
> - Afficher le texte des messages pr=E9c=E9dents -

Dear Andreas,

Congratulations : you crunched and squeezed my awful formula
more then can FullSimplify !
Could you please spare a few moments to explain
(for those like me who are not very familiar with EllipticK)
the way you did it ?