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Spherical Harmonics: Difference between revisions
→Definition
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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 Sloan<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>. You can also find alternative equations in DLMF<ref name="dlmf">Digital Library of Mathematical Functions, 14.30. [https://dlmf.nist.gov/14.30 https://dlmf.nist.gov/14.30]</ref>. | ||
There are <math>2l+1</math> functions for each band. | There are <math>2l+1</math> functions for each band. | ||