Extension of the scalar spherical harmonics for use with vector fields
In mathematics, vector spherical harmonics (VSH) are an extension of the scalar spherical harmonics for use with vector fields. The components of the VSH are complex-valued functions expressed in the spherical coordinate basis vectors.
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expanded into radiating sphericalvectorsphericalharmonics. The internal field is expanded into regular vectorsphericalharmonics. By enforcing the boundary...
This is a table of orthonormalized sphericalharmonics that employ the Condon-Shortley phase up to degree ℓ = 10 {\displaystyle \ell =10} . Some of these...
zonal sphericalharmonics are special sphericalharmonics that are invariant under the rotation through a particular fixed axis. The zonal spherical functions...
derivatives of a vector-valued function List of canonical coordinate transformations Sphere – Set of points equidistant from a center Sphericalharmonic – Special...
sphericalharmonics. The vector Laplace operator, also denoted by ∇ 2 {\displaystyle \nabla ^{2}} , is a differential operator defined over a vector field...
standard lighting equations with spherical functions that have been projected into frequency space using the sphericalharmonics as a basis. To take a simple...
vectors. A special class of these are spherical tensor operators which apply the notion of the spherical basis and sphericalharmonics. The spherical...
expansions in sphericalharmonics with coefficients proportional to the spherical Bessel functions. However, applying this expansion to each vector component...
In vector calculus, divergence is a vector operator that operates on a vector field, producing a scalar field giving the quantity of the vector field's...
VSH may refer to: Vectorsphericalharmonics Very smooth hash, in cryptography VSH News, a Pakistani television station XrossMediaBar (Sony codename: VSH)...
dependence of radiation is recovered. Multipole expansion SphericalharmonicsVectorsphericalharmonics Near and far field Quadrupole formula Hartle, James...
In physics and mathematics, the solid harmonics are solutions of the Laplace equation in spherical polar coordinates, assumed to be (smooth) functions...
conditions, for which the solutions represent standing waves, or harmonics, analogous to the harmonics of musical instruments. The wave equation in one space dimension...
often partially replaced by cubic harmonics for a number of reasons. These harmonics are usually named tesseral harmonics in the field of condensed matter...
needs. Furthermore, there was no widely accepted formulation of sphericalharmonics for acoustics, so one was borrowed from chemistry, quantum mechanics...
In vector calculus, the gradient of a scalar-valued differentiable function f {\displaystyle f} of several variables is the vector field (or vector-valued...
mechanics and sphericalharmonic functions. While spherical polar coordinates are one orthogonal coordinate system for expressing vectors and tensors using...
portal Harmonic function Sphericalharmonics Zonal sphericalharmonics Multilinear polynomial Walsh, J. L. (1927). "On the Expansion of Harmonic Functions...
symmetry group O(3) as a certain multipole (or the corresponding vectorsphericalharmonic), but does not radiate to the far field. In photonics, anapoles...
polynomials or wavelets for instance, and in higher dimensions into sphericalharmonics. For instance, if en are any orthonormal basis functions of L2[0...
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