Integrals involving associated legendre polynomials

Do the following integrals have a closed-form solution for any integer value of $m,l,k$ and $n$?

$\int^{\pi}_{0} P^{m}_{l}\left(\cos\theta\right)P^{n}_{k}\left(\cos\theta\right)\cot\theta d\theta$

$\int^{\pi}_{0} P^{m}_{l}\left(\cos\theta\right)P^{n}_{k}\left(\cos\theta\right)\frac{1}{\sin\theta} d\theta$

• What do you mean by "non-singular solution"? The integrals are singular, but if they converge, they just have a solution. Maybe you mean "closed form"? – Wolfgang Aug 9 '16 at 19:26
• Surely you are integrating from on $[0,\pi]$ rather than $[-1,1]$? In any case I'd change variables to $x=\cos\theta$. – Lior Silberman Aug 9 '16 at 20:45