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Spherical Harmonics are defined as[5]:

$\begin{matrix} Y_l^m(\theta, \varphi) &=& \sqrt{\frac{(2l + 1)}{4 \pi}\;\frac{(l-m)!}{(l+m)!}} \;P_l^m(\cos{\theta})\; e^{im\varphi} \\ &=& \sqrt{\frac{2}{4 \pi}}\; N_l^m(\cos{\theta})\; e^{im\varphi} \end{matrix}$ $\text{ where } P_l^m \text{ and } N_l^m \text{ are respectively Associated and Normalized Legendre Polynomial}$

Spherical Harmonics Transform