Laguerre differential equation
= Laguerre differential equation
{c}
{title2=$xy''+(1-x)y'+\nu y=0$}
This equation has a <regular singular point> at zero and an <irregular singular point> at infinity. For a nonnegative integer $\nu=n$, the solution analytic at zero with value one is the <Laguerre polynomial> $L_n$. Its weighted <self-adjoint> form is $(xe^{-x}y')'+\nu e^{-x}y=0$, connecting it to the <Laguerre differential operator on polynomials>.