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Re: Integrate Bug

  • To: mathgroup at smc.vnet.net
  • Subject: [mg100673] Re: Integrate Bug
  • From: Valeri Astanoff <astanoff at gmail.com>
  • Date: Wed, 10 Jun 2009 17:13:01 -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,

Good day,

Here is the most compact form of the integral,
due to Dr. Andreas Dieckmann, who e-mailed me
he used "transformations (17.4.3), (17.4.11)
and (17.4.15) given in Abramowitz/Stegun" :

4*EllipticK[(4*b*Sqrt[a^2 + z^2])/(b + Sqrt[a^2 + z^2])^2]/(b + Sqrt
[a^2 + z^2])

--
Valeri Astanoff

p.s. I'm a bit disappointed FullSimplify couldn't do the same...


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