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I have the following problem: I need to evaluate the integral $$\int_{\cos(\alpha)}^1 P_l(t)P_{l'}(t) \, dt $$ for $\alpha \in [0,\pi]$ and each combination of $l$ and $l'$, where $P_l$ is the $l$-th ...

I am interested in evaluating some elliptic integrals, and I have not been able to secure a reference to do exactly what I need. Most of the references I've found seem to focus on reducing more ...