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 $t\in\mathbb{R}$.

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

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