Hello, I'm trying to show that Integral[x*J0(a*x)*J0(a*x), from 0 to 1] = 1/2 * J1(a)^2 Here, (both) a's are the same and they are a root of J0(x). I.e., J0(a) = 0. I have found and can do the case where you have two different roots, a and b, and the integral evaluates to zero (orthogonality). How do I go about showing this relationship? I can't find details anywhere.