# Solutions of legendre equation for $\vert x\vert \leq 1$

Why books say that is necessary in Legendre equation to have $l$ integer if you want regular solutions in $\vert x\vert \leq 1$. It seems not necessary.

"It seems not necessary." - what gave you the idea? Both kinds of Legendre functions will necessarily display singularities at $\pm 1$, with the notable exception of the Legendre polynomials (and that bit has a whole lot to do with the integer restriction)... –  Ｊ. Ｍ. Nov 8 '12 at 6:27