# Normalization of Bessel Functions

1. Oct 18, 2009

### Pengwuino

Jackson 3.16 has one derive the orthonormality of the bessel functions, that is:

$$\int\limits_0^\infty {\rho J_v (kp)J_v (k'p)d\rho } = \frac{{\delta (k - k')}}{k}$$

Now, I was able to show that infact, they are orthogonal, but I haven't been able to figure out the 1/k term. Basically, I'm looking to see what

$$\int\limits_0^\infty {\rho J_v (kp)J_v (k'p)d\rho } = N\delta (k - k')$$

produces where N is the normalization constant that I need to determine. I've been stumped on how to show that the normalization constant is infact, 1/k. Any ideas anyone? :)