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Integration of Bessel function

  1. Jul 11, 2010 #1
    1. The problem statement, all variables and given/known data
    Hi, I need to integrate this:
    [tex]\int[/tex](J0(r))2rdr between 0<r<a
    It is for calculating the energy of a nondiffracting beam inside a radius of a. (the r is because of the jacobian in polar coordinates)

    3. The attempt at a solution
    I saw somewhere that said the integral was a known one and it didn't even bother to write it down but couldn't find it anywhere else
    I think it might be found also in Ballanis:antenna theory but I can't find the book

    Thanks in advance
    Last edited: Jul 11, 2010
  2. jcsd
  3. Jul 11, 2010 #2


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    Science Advisor

    Mathematica says that:
    [tex]\int^a_0J_0(r)^2 rdr = \frac{a^2}{2}(J_0(a)^2+J_1(a)^2)[/tex]
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