       Re: Integrate Bug

• To: mathgroup at smc.vnet.net
• Subject: [mg100588] Re: Integrate Bug
• From: Valeri Astanoff <astanoff at gmail.com>
• Date: Mon, 8 Jun 2009 06:17:50 -0400 (EDT)
• References: <gv2jh5\$97b\$1@smc.vnet.net> <h0btr4\$8ju\$1@smc.vnet.net>

```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 the
>
> > 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

```