My question concerns the associated or generalized Legendre polynomials. They are labeled by two numbers $m$ and $l$; i.e., $P_l^m(x)$, for $x \in [-1,1]$. Usually one assumes that $m$ and $l$ are both integers, but I suspect that it is possible for them to be half integers. If this is correct, what is the meaning of formulas like
$$P_l^{-m}(x)=(-1)^m \frac{(l-m)!}{(l+m)!}P_l^m(x)$$
or Rodrigues's formula?
Thanks