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sphericalHarmonics

sphericalHarmonics (L, M, θ, φ)​

The sphericalHarmonics function returns the complex-valued spherical harmonics

YLM(θ,ϕ)=(−1)M2L+14π(L−M)!(L+M)!PLM(cos⁡(θ))eiMϕ,\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

PLM(cos⁡(θ))\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.