sphericalHarmonics

sphericalHarmonics (L, M, θ, φ)

The sphericalHarmonics function returns the complex-valued spherical harmonics

$$\displaystyle Y_{L}^{M}(\theta, \phi)=(-1)^{M} \sqrt{\frac{2 L+1}{4 \pi} \frac{(L-M)!}{(L+M)!}} P_{L}^{M}(\cos (\theta)) e^{i M \phi},$$

where

$$\displaystyle P_{L}^{M}(\cos (\theta))$$

is the associated Legendre function.

See Also

legendreA

Demos

Open Spherical Harmonics Demo

Open Numerical Integation Demo

References

Arfken, G., Mathematical Methods for Physicists, Academic Press, New York, 1985.