I want to prove orthogonality of associated Legendre polynomial.
In my textbook or many posts,
\int^{1}_{-1} P^{m}_{l}(x)P^{m}_{l'}(x)dx = 0 (l \neq l')
is already proved.
But, for upper index m,
\int^{1}_{-1} P^{m}_{n}(x)P^{k}_{n}(x)\frac{dx}{ ( 1-x^{2} ) } = 0 (m \neq k)
is not...