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Multipole expansion

A multipole expansion is a mathematical series representing a function that depends on angles—usually the two angles used in the spherical coordinate system (the polar and azimuthal angles) for three-dimensional Euclidean space, R 3 {\displaystyle \mathbb {R} ^{3}} . Multipole expansions are useful because, similar to Taylor series, often times only the…

Applications, General mathematical properties & Interaction of two non-overlapping charge distributions

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Overview

Expansion in spherical harmonics

Applications

Multipole expansion of a potential outside an electrostatic charge distribution

Interaction of two non-overlapping charge distributions

Examples

General mathematical properties

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Multipole expansion

Nodes96
Edges95
Triples53
Avg. degree1.98
Density0.020833
Components1

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Multipole expansion

Top relations

related to Interaction of two non-overlapping charge distributions · 20
Multipole expansion → AB, Ai, Bj, Clebsch, Consider, Further, Gordan, In, Laplace, LM, M-, Note, Qm, The, Think, This, UAB, Under, Use, We
related to Multipole expansion of a potential outside an electrostatic charge distribution · 10
Multipole expansion → Also, Cartesian, Consider, Its, Legendre, Taylor, The, The Cartesian, Two, We
related to Expansion in spherical harmonics · 7
Multipole expansion → Equivalently, Here, If, In, Most, The, Thus
has application · 6
Multipole expansion → Ewald, Greengard, Multipole, Rokhlin, The, Truncation
related to Spherical form · 5
Multipole expansion → Laplace, Note, The, Thus, We
related to General mathematical properties · 4
Multipole expansion → Even, Multipole, One, These
is a · 1
Multipole expansion → mathematical series representing a function that depends on angles

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Important terminology

multipole displaystyle expansion sum spherical mathbf charge function ell terms potential moments frac distribution real harmonics two dipole equiv charges

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Multipole expansionis amathematical series representing a function that depends on angles0.90text
Multipole expansionhas applicationMultipole0.60section
Multipole expansionhas applicationThe0.60section
Multipole expansionhas applicationTruncation0.60section
Multipole expansionhas applicationGreengard0.60section
Multipole expansionhas applicationRokhlin0.60section
Multipole expansionhas applicationEwald0.60section
Multipole expansionrelated to Expansion in spherical harmonicsMost0.60section
Multipole expansionrelated to Expansion in spherical harmonicsThus0.60section
Multipole expansionrelated to Expansion in spherical harmonicsThe0.60section
Multipole expansionrelated to Expansion in spherical harmonicsEquivalently0.60section
Multipole expansionrelated to Expansion in spherical harmonicsHere0.60section

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