y_l^m(\theta, \phi) = \begin{Bmatrix}\sqrt{2}K_l^mcos(m\phi)P_l^m(cos\theta), && m>0 \\ \sqrt{2}K_l^mcos(-m\phi)P_l^{-m}(cos\theta), && m<0 \\ K_l^0 P_l^0(cos\theta), && m=0 \end{Bmatrix}
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