# Integration of Bessel function

1. Jul 11, 2010

### johnsmi

1. The problem statement, all variables and given/known data
Hi, I need to integrate this:
$$\int$$(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

$$\int^a_0J_0(r)^2 rdr = \frac{a^2}{2}(J_0(a)^2+J_1(a)^2)$$