Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Integrals with bessel functions

  1. Mar 4, 2009 #1
    I am trying to solve

    int(int(exp(a*cos(theta)*sin(phi))*sin(phi), phi = 0 .. Pi), theta = 0 .. 2*Pi) (1)

    with a a constant.

    Using the second last definite integral on


    the integral (1) reduces to

    2*Pi*(int(sin(phi)*BesselI(0, a*sin(phi)), phi = 0 .. Pi)) (2)

    Can anyone solve (1) or (2)?
  2. jcsd
  3. Mar 5, 2009 #2

    Plugging it into Mathematica assuming a>0 gives 4*Pi*Sinh[a]/a.

    It doesn't tell the steps used, unfortunately :)
  4. Mar 5, 2009 #3

    Apparently, Mathematica is the only program that can solve several of the integrals I am dealing with out of the box. Unfortunately, I do not have access to Mathematica.

    Would you please be so kind to try if Mathematica can solve

    int(exp(a*cos(phi))*(sin(phi))^2, phi = 0 .. Pi)

    with a a positive real constant?
  5. Mar 5, 2009 #4
    The integral

    assume(a > 0);
    int(exp(a*cos(phi))*sin(phi)^2, phi = 0 .. Pi);

    equals to


    I have solved the integral using Mathematica, which seems to solve all these integrals out of the box.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook