1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Is this a known function ?

  1. Jul 11, 2011 #1
    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.

  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.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook