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Is this a known function ?

  1. Jul 11, 2011 #1
    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.
     
  2. jcsd
  3. Jul 11, 2011 #2
    Last edited by a moderator: Apr 26, 2017
  4. Jul 12, 2011 #3
    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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