# Difference between revisions of "Spherical harmonics"

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The '''spherical harmonics''' <math>Y_l^m (\theta,\phi)</math> are the angular portion of the solution to [[Laplace's equation]] in spherical coordinates. | The '''spherical harmonics''' <math>Y_l^m (\theta,\phi)</math> are the angular portion of the solution to [[Laplace's equation]] in spherical coordinates. | ||

+ | They are given by | ||

+ | :<math>Y_l^m (\theta,\phi) = | ||

+ | (-1)^m \sqrt{\frac{2n+1}{4\pi}\frac{(n-m)!}{(n+m)!}} | ||

+ | P^m_n(\cos\theta) e^{i m \phi},</math> | ||

+ | where <math> P^m_n </math> is the [[associated Legendre function]]. | ||

+ | |||

The first few spherical harmonics are given by: | The first few spherical harmonics are given by: | ||

## Latest revision as of 12:54, 20 June 2008

The **spherical harmonics** are the angular portion of the solution to Laplace's equation in spherical coordinates.
They are given by

where is the associated Legendre function.

The first few spherical harmonics are given by:

## See also[edit]

## References[edit]

- M. E. Rose "Elementary theory of angular momentum", John Wiley & Sons (1967) Appendix III
- I. Nezbeda, J. Kolafa and S. Labík "The spherical harmonic expansion coefficients and multidimensional integrals in theories of liquids", Czechoslovak Journal of Physics
**39**pp. 65-79 (1989)