Solid Harmonics
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High Quality Content by WIKIPEDIA articles! 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: R^m_ell(mathbf{r}) = r^ell Y^m_ell(theta,phi).

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High Quality Content by WIKIPEDIA articles! 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: R^m_ell(mathbf{r}) = r^ell Y^m_ell(theta,phi).