Happy to help. Polynomial basis sets are fascinating and useful, but t is definitely be hard to teach them in a way that doesn't put students to sleep.
They are different only in the normalization constant. The x-dependence of P_l^m is the same as that of P_l^−m. If the normalization constant is important, then you can use this equation: P_l^−m = P_l^m * (l-m)! / (l+m)!
