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Re: Re: How to simplify to a result that is real
*To*: mathgroup at smc.vnet.net
*Subject*: [mg50750] Re: [mg50735] Re: How to simplify to a result that is real
*From*: DrBob <drbob at bigfoot.com>
*Date*: Sun, 19 Sep 2004 03:55:58 -0400 (EDT)
*References*: <cidt38$brv$1@smc.vnet.net> <200409180948.FAA00572@smc.vnet.net>
*Reply-to*: drbob at bigfoot.com
*Sender*: owner-wri-mathgroup at wolfram.com
It's interesting that the output of ComplexExpand[ch, TargetFunctions -> {Re, Im}] in this case doesn't include Re or Im. What is ComplexExpand really doing, here?
Bobby
On Sat, 18 Sep 2004 05:48:55 -0400 (EDT), Peter Valko <p-valko at tamu.edu> wrote:
> Richard Chen <richard at doubleprime.com> wrote in message news:<cidt38$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
>
>
>
--
DrBob at bigfoot.com
www.eclecticdreams.net
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