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How to solve this Bessel integral?

  1. Sep 2, 2008 #1

    Do you have any idea to solve this integral?

    \int^{\phi_{1}}_{\phi_{2}} exp[j cos(x)] dx

    where \phi_{1} and \phi_{2} are an arbitrary angles. If \phi_{1}=\pi and \phi_{2}=0, the answer for this integral is a Bessel function.


  2. jcsd
  3. Sep 3, 2008 #2


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    Use the identity

    [tex]e^{ iz\cos\phi} = \sum_{s=-\infty}^{\infty}i^sJ_s(z)e^{is\phi}[/tex]
  4. Sep 4, 2008 #3
    Thank you very much. Do you have the reference for this equation since I do not find it in my mathematical books?
  5. Sep 4, 2008 #4


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