Does an analytic solution exist for this integral

christianjb
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(not a HW problem- I'm writing a paper)

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

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