Is this a known function ?

  • Thread starter mnb96
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  • #1
713
5
Hello,
while attempting to solve a problem, I came up with the following integral:

[tex]\int_0^{2\pi}e^{i\left( u\cos(x)+v\sin(x) \right)}dx[/tex]

where u,v are two real constants.
I don't know how to solve this definite integral and I am wondering if this formula is already known, and if it pops up in other contexts.

Thanks.
 

Answers and Replies

  • #3
713
5
Thanks a lot!
It seems the definite integral of that expression is given by a 0-order 'modified Bessel function'. Interesting.

I trust the answer from that site but I am wondering now if it would be difficult to prove that result.
 

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