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MathGroup Archive 2005

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Re: Integration problem

  • To: mathgroup at smc.vnet.net
  • Subject: [mg60495] Re: Integration problem
  • From: Peter Pein <petsie at dordos.net>
  • Date: Sun, 18 Sep 2005 01:15:50 -0400 (EDT)
  • References: <200509160936.FAA05066@smc.vnet.net> <dggdma$gea$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Heidi.Foerster at physics.unige.ch schrieb:
> Hi,
> 
> I have a periodic function
> f=1\(2pi) (1-e^{-2a})/(1-2e^{-a}cos(x-x0)+e^{-2a}), and I want to
> calculate the first Fourier coefficient, which corresponds to
> Integrate[f cos(x),{x,0,2pi}].
> 
> The result mathematica tells me is -Cos[x0] Sinh[a].
> (The correct result would be Cos[x0] e^{-a}.)
> 
> If I set x0 to zero, I get the correct result e^{-a}:
> Simplify[Integrate[(f /. x0 -> 0) Cos[x], {x, 0, 2 \[Pi]}], a > 0]
> e^{-a}
> 
> The problem is, that for x0=0 both outputs don't match.
> Can anyone tell me what's wrong?
> 
> Heidi
> 
Hello Heidi,

 it seems, Mathematica has difficulties to select the correct branch(es)
 while integrating. With a little luck, one succeeds with:

SetOptions[Simplify,
  TransformationFunctions -> {PowerExpand, Automatic}];
a0 = Integrate[f*Cos[x], {x, 0, 2*Pi},
  Assumptions -> a>0 && Element[x0,Reals]]

Cos[x0]/E^a

Peter

-- 
Peter Pein, Berlin
GnuPG Key ID: 0xA34C5A82
http://people.freenet.de/Peter_Berlin/


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