Central Forces Notes Section 31 $${R_n}^\ell (r){Y_\ell }^m\left( \theta ,\phi \right) = \sqrt { { {\left( {\frac{2}{{n{a_0} } } } \right)}^3}\frac{{\left( {n - \ell - 1} \right)!} }{{2n{ {\left( {\left( {n + \ell } \right)!} \right)}^3} } } } {\left( {\frac{{2r} }{{n{a_0} } } } \right)^\ell }{e^{ - \frac{r}{ {n{a_0} } } } }L_{n + \ell }^{2\ell + 1}\left( {\frac{ {2r} }{ {n{a_0} } } } \right){Y_\ell }^m\left( {\theta ,\phi } \right)$$