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MathGroup Archive 2005

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Integration problem

  • To: mathgroup at smc.vnet.net
  • Subject: [mg60467] Integration problem
  • From: Heidi.Foerster at physics.unige.ch
  • Date: Sat, 17 Sep 2005 02:31:48 -0400 (EDT)
  • References: <200509160936.FAA05066@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

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


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