# Fourier Bessel series

## Homework Statement

By appropriate limiting procedures prove the following expansion
$$\frac{1}{\left(\rho^2+z^2\right)^{1/2}}=\int^{\infty}_{0} e^{-k\left|z\right|}J_{0}(k\rho)dk$$

## The Attempt at a Solution

I tried to implicate the fourier-bessel series but it turned out that there is no k dependence on coefficients of the series.

What can I do to proceed this question?