Is there any formula for computing the following integral $$\int_a^1(P^m_l)^2(x)\,dx \, ,\text{with} -1<a<1$$ where $P^m_l$ is the associated Legendre's function (of the first kind) of order $m\in\mathbb{N}$ and of degree $l=-0.5+it$ with $t\in\mathbb{R}$.