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

**Follow-Ups**:**Re: Re: Re: How to simplify to a result that is real***From:*Andrzej Kozlowski <andrzej@akikoz.net>

**References**:**Re: How to simplify to a result that is real***From:*p-valko@tamu.edu (Peter Valko)