Spherical Harmonics

$Y_l^m(\theta ,\varphi )=A_l^m{\Phi }^m(\varphi ){\Theta }_l^m(\theta )$

$A_l^m=\sqrt{\frac{(2l+1)(l-m)!}{4\pi (l+m)!}}$

• Normalization constant

$\Phi (\varphi )=e^{im\varphi }$

• Azimuthal angle

$\Theta (\theta )=P_l^m(\cos \theta )$

• Altitude angle
• $P_l^m$ is the associated Legendre polynomial