Other orthogonal polynomials, Laguerre polynomials
These polynomials arise from the solution of the differential
equation
\begin{equation*}
\left(\frac{d^2 }{dx^2}-\frac{d }{dx}+\frac{\lambda}{x}-\frac{l(l+1)}{x^2}\right){\cal L}(x)=0,
\end{equation*}
where
l is an integer
l\ge 0 and
\lambda a constant. This equation
arises for example from the solution of the radial Schr\"odinger equation with
a centrally symmetric potential such as the Coulomb potential.