Definition:Surface Harmonic
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This page is about Surface Harmonic. For other uses, see harmonic.
Definition
A surface harmonic is a spherical harmonic:
- $r^n \paren {a_n \map {P_n} {\cos \theta} + \ds \sum_{m \mathop = 1}^n \paren { {a_n}^m \cos m \phi + {b_n}^m \sin m \phi} \map { {P_n}^m} {\cos \theta} }$
such that $r = 1$.
That is:
- $a_n \map {P_n} {\cos \theta} + \ds \sum_{m \mathop = 1}^n \paren { {a_n}^m \cos m \phi + {b_n}^m \sin m \phi} \map { {P_n}^m} {\cos \theta}$
Also see
- Results about surface harmonics can be found here.
Sources
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): harmonic
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): harmonic: 2.