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Integration problem

  • To: mathgroup at
  • Subject: [mg60467] Integration problem
  • From: Heidi.Foerster at
  • Date: Sat, 17 Sep 2005 02:31:48 -0400 (EDT)
  • References: <>
  • Sender: owner-wri-mathgroup at


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]

The problem is, that for x0=0 both outputs don't match.
Can anyone tell me what's wrong?


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