Laguerre polynomials

Summary

The Laguerre polynomials $L_n^{(\alpha)}$ are the classical orthogonal polynomials on the half-line $[0, \infty)$ for the weight $x^\alpha e^{-x}$. The case $\alpha = 0$ gives the ordinary Laguerre polynomials $L_n$. They solve the Laguerre differential equation. They appear in the radial wave functions of the hydrogen atom and in Gaussian quadrature on $[0, \infty)$.