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Solid harmonics

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…

Derivation, relation to spherical harmonics, Real form & Addition theorems

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Derivation, relation to spherical harmonics

Addition theorems

Complex form

Real form

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Solid harmonics

Nodes29
Edges28
Triples26
Avg. degree1.93
Density0.068966
Components1

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Solid harmonics

Top relations

related to Complex form · 9
Solid harmonics → Delta, If, Laplace, Note, One, Separating, SO, The, These
related to Linear combination · 7
Solid harmonics → Condon, Legendre, Shortley, Since, The, Theta, We
related to Addition theorems · 4
Solid harmonics → Clebsch, Clebsch-Gordan, Gordan, The
related to Real form · 4
Solid harmonics → By, Cartesian, The, They
is a · 2
Solid harmonics → same. z-dependent partUpon writing u, same.z-dependent partUpon writing u

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Important terminology

displaystyle ell harmonics frac solid left right equiv pi spherical theta mathbf functions -1 -m regular varphi cos sin sum

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Solid harmonicsis asame.z-dependent partUpon writing u0.90text
Solid harmonicsis asame. z-dependent partUpon writing u0.90text
Solid harmonicsrelated to Addition theoremsThe0.60section
Solid harmonicsrelated to Addition theoremsClebsch0.60section
Solid harmonicsrelated to Addition theoremsGordan0.60section
Solid harmonicsrelated to Addition theoremsClebsch-Gordan0.60section
Solid harmonicsrelated to Complex formThe0.60section
Solid harmonicsrelated to Complex formLaplace0.60section
Solid harmonicsrelated to Complex formDelta0.60section
Solid harmonicsrelated to Complex formSeparating0.60section
Solid harmonicsrelated to Complex formOne0.60section
Solid harmonicsrelated to Complex formNote0.60section

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