Spherical Harmonics

#Physics

$\displaystyle Y_{l}^{m}(\theta,\phi)=A^{m}{l}\Phi^{m}(\phi)\Theta^{m}{l}(\theta)$

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

• Normalization constant

$\displaystyle \Phi(\phi)=e^{im\phi}$

• Azimuthal angle

$\displaystyle \Theta(\theta)=P_{l}^{m}(\cos \theta)$

• Altitude angle
• $\displaystyle P_{l}^{m}$ is the associated Legendre polynomial