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MathGroup Archive 2004

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Re: How to simplify to a result that is real

  • To: mathgroup at smc.vnet.net
  • Subject: [mg50735] Re: How to simplify to a result that is real
  • From: p-valko at tamu.edu (Peter Valko)
  • Date: Sat, 18 Sep 2004 05:48:55 -0400 (EDT)
  • References: <cidt38$brv$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Richard Chen <richard at doubleprime.com> wrote in message news:<cidt38$brv$1 at smc.vnet.net>...
> The command:
> 
> Integrate[1/(1 + e Cos[t]), {t, 0, a}, 
>   Assumptions -> {-1 < e < 1, 0 < a < Pi}]
> 
> leads to a complex valued result. I could not make
> mathematica to render the result in a form that is
> purely real. ComplexExpand, Refine all do not seem to work.
> 
> Does anyone know how to make mathematica to simplify this
> result into a real form?
> 
> Thanks for any info.
> 
> Richard



Richard,

I think this will work:


ch = Integrate[1/(1 + e Cos[t]), {t, 0, a}, Assumptions -> {-1 < e <
1, 0 < a < Pi}]

FullSimplify[ComplexExpand[ch, TargetFunctions -> {Re, Im}], {-1 < e <
1, 0 < a < Pi}]


The result is

(-2*ArcTan[((-1 + e)*Tan[a/2])/Sqrt[1 - e^2]])/Sqrt[1 - e^2]


Peter


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