## Legendre Functions, Spherical Rotations, and Multiple Elliptic Integrals    [PDF]

Yajun Zhou
A closed-form formula is derived for the generalized Clebsch-Gordan integral $\int_{-1}^1 {[}P_{\nu}(x){]}^2P_{\nu}(-x)\D x$, with $P_\nu$ being the Legendre function of arbitrary complex degree $\nu\in\mathbb C$. The finite Hilbert transform of \$ P_{\nu}(x)P_{\nu}(-x),-1View original: http://arxiv.org/abs/1301.1735