Solid harmonics

In physics and mathematics, the solid harmonics are solutions of the Laplace equation in spherical polar coordinates. There are two kinds: the regular solid harmonics $R^m_\ell(\mathbf{r})$ , which vanish at the origin and the irregular solid harmonics $I^m_{\ell}(\mathbf{r})$ , which are singular at the origin. Both sets of functions play an important role in potential theory, and are obtained by rescaling spherical harmonics appropriately:

单词	Solid spherical harmonics
释义	Solid spherical harmonics 英语百科 Solid harmonics In physics and mathematics, the solid harmonics are solutions of the Laplace equation in spherical polar coordinates. There are two kinds: the regular solid harmonics $R^m_\ell(\mathbf{r})$ , which vanish at the origin and the irregular solid harmonics $I^m_{\ell}(\mathbf{r})$ , which are singular at the origin. Both sets of functions play an important role in potential theory, and are obtained by rescaling spherical harmonics appropriately:
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Solid spherical harmonics

Solid harmonics