An Integral Involving the Product of Bessel Function and Associated Laguerre Polynomial
Question: Try to prove the following integral: [\int_{0}^{\infty} z^{\mu/2} \mathrm{e}^{-z} L_{n}^{\mu}(z)J_{\mu}\left(2\sqrt{xz}\right) \mathrm{d}z = \frac{1}{n!} x^{n+\mu/2}\mathrm{e}^{-x},] wh...