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.
Thanks in advance.
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1"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. ain't a mathematician Nov 08 '12 at 06:27