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Re: Integrate Bug

  • To: mathgroup at smc.vnet.net
  • Subject: [mg100451] Re: Integrate Bug
  • From: Valeri Astanoff <astanoff at gmail.com>
  • Date: Thu, 4 Jun 2009 03:33:54 -0400 (EDT)
  • References: <gv2jh5$97b$1@smc.vnet.net>

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


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