In physics and mathematics, the solid harmonics are solutions of the Laplace equation in spherical polar coordinates, assumed to be (smooth) functions R 3 → C {\displaystyle \mathbb {R} ^{3}\to \mathbb {C} } . There are two kinds: the regular solid harmonics R ℓ m ( r ) {\displaystyle R_{\ell }^{m}(\mathbf {r} )} , which are well-defined at the origin and the irregular solid harmonics I ℓ m ( r ) {\displaystyle I_{\ell }^{m}(\mathbf {r} )} , which are singular at the origin.
In physics and mathematics, the solid harmonics are solutions of the Laplace equation in spherical polar coordinates, assumed to be (smooth) functions R 3 → C {\displaystyle \mathbb {R} ^{3}\to \mathbb {C} } . There are two kinds: the regular solid harmonics R ℓ m ( r ) {\displaystyle R_{\ell }^{m}(\mathbf {r} )} , which are well-defined at the origin and the irregular solid harmonics I ℓ m ( r ) {\displaystyle I_{\ell }^{m}(\mathbf {r} )} , which are singular at the origin.
Source: Wikipedia "Solid harmonics" · CC BY-SA 4.0
Share this article: X · Bluesky