“Laplace Series”的概念、定义、习题解题方法及翻译-数学辞典

单词

Laplace Series

释义

Laplace Series

A 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

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)

and

are given by

			(8)
			(9)

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