Definition:Surface Harmonic

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.