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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
> > 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


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