# Integral of Legendre's function

Is there any formula for computing the following integral $$\int_a^1(P^m_l)^2(x)\,dx \, ,\text{with} -1 where $$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}$$.

• Similar question: mathoverflow.net/q/366081 – Max Alekseyev Aug 12 at 2:53
• with that $a$ in there, you are asking for the indefinite integral. – Gerald Edgar Aug 12 at 10:42
• the variable $a$ belongs to $(-1;1)$. – rihani Aug 12 at 11:43