When we think about the Fourier transform in two dimensional polar coordinates, the Hankel transform is the transformation with respect to the polar diameter. Now I have a question, why is the following expression invariant for the Hankel transform? And How to prove this equation?

$\exp \left(-\frac{1}{2} x\right) x^{m / 2} L_{p}^{m}(x)=\frac{1}{2}(-1)^{p} \int_{0}^{+\infty} \mathrm{d} y \exp \left(-\frac{1}{2} y\right) J_{m}(\sqrt{x y}) y^{m / 2} L_{p}^{m}(y)$

$L_{p}^{m}(y)$ is Laguerre function. m, p is order;

$J_{m}(\sqrt{x y})$ is Bessel function with order of m.