A note on spherical harmonics. (Q1529227)
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scientific article; zbMATH DE number 2685386
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A note on spherical harmonics. |
scientific article; zbMATH DE number 2685386 |
Statements
A note on spherical harmonics. (English)
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1893
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Ist \(U_n\) eine beliebig gegebene ganze homogene Function von \(x, y, z\) vom Grade \(n\), so kann man in der Reihe \[ V = U_n+r^2U_{n-2}+r^4U_{n-4}+\cdots \] \[ (r = \sqrt{x^2+y^2+z^2}) \] die Coefficienten \(U_{n-2}\), \(U_{n-4}\) etc. stets so bestimmen, dass \(V\) der Laplace'schen Differentialgleichung \(\varDelta^2 V= 0\) genügt. Der Satz wird bewiesen und an Beispielen erläutert.
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