My textbook says Laguerre's Equation $ xy''+(1-x)y'+ay =0 $ has singularities at $ x=0$ and $x=\infty. $
However, rearranging the equation gives $ y''+\frac{(1-x)}{x}y'+\frac{a}{x}y =0 $, and neither $ \frac{(1-x)}{x} $ nor $ \frac{a}{x} $ diverge at $ x = \infty $.
Do we just assume it diverges at $ x=\infty $? Or is it to do with dividing by $x$?