Chapter 12.10, Problem 8P

Write (10.7) with $m$ replaced by $-m;$ then use Problem 7 to show that $P_l^{-m}(x)={(-1)}^m\frac{(l-m)!}{(l+m)!}{P}_l^m(x)$.

Comment: This shows that (10.7) is a solution of (10.1) when m is negative.