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Does an analytic solution exist for this integral

  1. Nov 5, 2007 #1
    (not a HW problem- I'm writing a paper)

    Looking for an analytic solution for the following- if one exists

    [tex]\frac{1}{2\pi}\int_0^{2\pi}e^{-cos^2(\theta)}d\theta[/tex]
     
  2. jcsd
  3. Nov 5, 2007 #2

    Avodyne

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    [tex]\frac{1}{2\pi}\int_0^{2\pi}e^{-2a \cos^2(\theta)}d\theta
    =e^{-a}I_0(a)[/tex]
    where [itex]I_0(a)[/itex] is a modified Bessel function, and a=1/2 in your case. But, as far as I know, [itex]I_0(1/2)[/itex] has no particular value in terms of other constants.
     
  4. Nov 5, 2007 #3
    Thanks. Is there a good web-reference for this? I'll try and track it down on Mathworld.
     
  5. Nov 5, 2007 #4

    Avodyne

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  6. Nov 5, 2007 #5
    Thanks, I found it.
     
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