- spherical harmonics
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The solutions to Laplaces equation using spherical coordinates
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spherical harmonics
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Spherical harmonics — In mathematics, the spherical harmonics are the angular portion of an orthogonal set of solutions to Laplace s equation represented in a system of spherical coordinates. Spherical harmonics are important in many theoretical and practical… … Wikipedia
Spin-weighted spherical harmonics — are generalizations of the standard spherical harmonics and like the usual spherical harmonics are complex functions on the sphere. These harmonics are typically denoted by {} sY {lm}, where s is the spin weight , and l and m are akin to the… … Wikipedia
Vector spherical harmonics — In mathematics, vector spherical harmonics (VSH) are an extension of the scalar spherical harmonics for the use with vector fields.DefinitionSeveral conventions have been used to define the VSH [R.G. Barrera, G.A. Estévez and J. Giraldo, Vector… … Wikipedia
Table of spherical harmonics — This is a table of orthonormalized spherical harmonics that employ the Condon Shortley phase up to degree l=10. Some of these formulas give the Cartesian version. This assumes x, y, z, and r are related to heta, and varphi, through the usual… … Wikipedia
Spherical multipole moments — are the coefficients in a series expansionof a potential that varies inversely with the distance R to a source, i.e., as frac{1}{R}. Examples of such potentials are the electric potential, the magnetic potential and the gravitational… … Wikipedia
Spherical harmonic lighting — Spherical harmonic (SH) lighting is a family of real time rendering techniques that can produce highly realistic shading and shadowing with comparatively little overhead. All SH lighting techniques involve replacing parts of standard lighting… … Wikipedia
Spherical function — can refer to* Spherical harmonics *Zonal spherical function … Wikipedia
Spherical coordinate system — In mathematics, the spherical coordinate system is a coordinate system for representing geometric figures in three dimensions using three coordinates: the radial distance of a point from a fixed origin, the zenith angle from the positive z axis… … Wikipedia
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… … Wikipedia
Cylindrical harmonics — In mathematics, the cylindrical harmonics are a set of linearly independent solutions to Laplace s differential equation, , expressed in cylindrical coordinates, ρ (radial coordinate), φ (polar angle), and z (height). Each function Vn(k) is the… … Wikipedia
