释义 |
Laplace SeriesA function expressed as a double sum of Spherical Harmonics is called a Laplace series. Taking as a Complex Function,
 | (1) |
Now multiply both sides by and integrate over and . | |  | | | (2) | Now use the Orthogonality of the Spherical Harmonics
 | (3) |
so (2) becomes
 | (4) |
where is the Kronecker Delta.
For a Real series, consider
 | (5) |
Proceed as before, using the orthogonality relationships | |  | (6) |
 | |  | (7) | So and are given by
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