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==Definition== | ==Definition== | ||
Spherical Harmonics are a set of orthonormal basis functions defined on the sphere. | Spherical Harmonics are a set of orthonormal basis functions defined on the sphere. | ||
Below are some explicit formulas for Laplace spherical harmonics stolen from <ref name="stupidsh">Peter-Pike Sloan, [http://www.ppsloan.org/publications/StupidSH36.pdf Stupid Spherical Harmonics (SH) Tricks]</ref> | Below are some explicit formulas for Laplace spherical harmonics stolen from Sloan<ref name="stupidsh">Peter-Pike Sloan, [http://www.ppsloan.org/publications/StupidSH36.pdf Stupid Spherical Harmonics (SH) Tricks]</ref>. | ||
There are <math>2l+1</math> functions for each band. | There are <math>2l+1</math> functions for each band. | ||
* <math>Y_l^m(\theta, \varphi) = K_l^m e^{i m \varphi} P_l^{|m|} \cos(\theta)</math> for <math>-l \leq m \leq l</math> | * <math>Y_l^m(\theta, \varphi) = K_l^m e^{i m \varphi} P_l^{|m|} \cos(\theta)</math> for <math>-l \leq m \leq l</math> |