I already prove the orthogonality condition of Bessel functions for discrete case ($0,b$).
$$\int_0^{b}\rho J_{\nu}(\chi_{\nu l}\rho/b)J_{\nu}(\chi_{\nu l'}\rho/b)d\rho = \frac{b^2}{2}[J_{\nu+1}(\chi_{\nu l})]^2\delta_{ll'}$$
Now, I need to prove that the orthogonality condition of Bessel Functions in the continuous case ($0,\infty$) can be written as:
$$\int_0^{\infty}\rho J_{\nu}(k\rho)J_{\nu}(k'\rho)d\rho = \frac{1}{k}\delta(k'-k)$$
With $\chi_{\nu l} = kb$ and $\chi_{\nu l´} = k'b$. But I don't know how to do it. Thank you for your help!!!
