Definition:Zonal Harmonic

This page is about zonal harmonic. For other uses, see harmonic.

Definition

Let $H$ be a spherical harmonic in the form:

$r^n \paren {a_n \map {P_n} {\cos \theta} + \ds \sum_{m \mathop = 1}^n \paren { {a_n}^m \cos m \phi + {b_n}^m \sin m \phi} \map { {P_n}^m} {\cos \theta} }$

The function $\map {P_n} {\cos \theta}$ is known as a zonal harmonic.

Also see

• Results about zonal harmonics can be found here.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): harmonic
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): zonal harmonic
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): harmonic: 2.
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): zonal harmonic