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Explore the main themes, entities and connections around Multipole expansion. Start with the topic map, then use the sections below for research and deeper semantic analysis.
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Applications
10 related topics
General mathematical properties
12 related topics
Interaction of two non-overlapping charge distributions
11 related topics
Overview
27 related topics
Key facts & relationships
High-confidence facts extracted from structured source data. Use them as anchors for further research.
Topics to explore
A structured outline of related entities, concepts and subtopics. Open any item to build a new map centered on it.Browse the full topic structure. Each item opens a new analysis centered on that subject.
Overview
- Mathematical series Series (mathematics)
- Function Function (mathematics)
- Angles Angle
- Spherical coordinate system
- Polar Polar coordinate system
- Azimuthal Azimuth
- Euclidean space
- Taylor series
- Real Real number
- Complex Complex number
- Electromagnetic Electromagnetic field
- Gravitational fields Gravitational field
- Radius
- Moments Moment (physics)
- Monopole Monopole (mathematics)
- Dipolar potential field Dipole
- Quadrupole
- Greek numeral prefixes Greek numerals
- Powers Exponentiation
- Converges Convergent series
- Differentiation Differentiation (mathematics)
- Infinitesimal
- Complex conjugate
- This article Spherical multipole moments
- Classical electrodynamics
- Quantum mechanical Quantum mechanics
- Integral
Expansion in spherical harmonics
- Spherical harmonics
- Unit vector
- Implicitly summed Einstein summation convention
- Scalar Scalar (mathematics)
- Tensors Tensor
- Vector potential
- Gravitational waves Gravitational wave
- Laurent series
- Electromagnetic potential Electromagnetic four-potential
Applications
- Masses Mass
- Electric Electric field
- Magnetic fields Magnetic field
- Electromagnetic waves Electromagnetic wave
- Atomic nuclei Atomic nucleus
- Fast multipole method
- Greengard Leslie Greengard
- Rokhlin Vladimir Rokhlin (American scientist)
- Particles Particle
- Ewald summation
Multipole expansion of a potential outside an electrostatic charge distribution
- Cartesian coordinates
- Spherical polar coordinates
- Legendre Adrien-Marie Legendre
- Laplace equation
- Kronecker delta
- Laplace expansion Laplace expansion (potential)
- Solid harmonic
- Spherical harmonic
- Unitary transformation Solid harmonics
- Coulomb's law
Interaction of two non-overlapping charge distributions
- Molecules Molecule
- Electrons Electron
- Clebsch–Gordan coefficient
- S-state Azimuthal quantum number
- Atomic number
- Wave function
- Expectation (expected) value Expectation value (quantum mechanics)
- Point group symmetry Molecular symmetry
- Irreducible representation
- Group Group (mathematics)
- Selection rules Selection rule
Examples
- Potentials Potential
- Series expansion
- Coordinates Coordinate system
- Symmetry
- Axial multipole moments
- Cylindrical multipole moments
- Electric potential
- Magnetic potential Magnetic scalar potential
- Gravitational potential
General mathematical properties
- Mathematics
- Mathematical physics
- Orthogonal basis
- Field Field (physics)
- Distribution theory Distribution (mathematics)
- Directional derivatives Directional derivative
- Differential equations Differential equation
- Irreducible representations Group representation
- Symmetry group
- Orthogonal
- Separation of variables
- Linearly combined Linear combination
Advanced semantic analysis
Deeper signals for content research, entity SEO and topical coverage. The plain-language headings explain what each technical view is useful for.
Map overview Semantic statistics
Number of nodes, edges, triples, density and central hubs. Use it to gauge the size and connectivity of the map.Multipole expansion
Nodes96
Edges95
Triples53
Avg. degree1.98
Density0.020833
Components1
How this topic connects Entity context
Quick relationship hints grouped by predicate. Useful for spotting recurring semantic connections around the current entity.See the strongest relationship patterns around the current topic before diving into the raw triples.
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
Important terminology Word statistics
Frequent words and multi-word phrases across the lead, headings, infobox and body. Useful for terminology coverage.Use these terms to understand the vocabulary surrounding the topic, not as a checklist for keyword stuffing.
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
Extracted RDF-like relationships with confidence and source. The table includes structured facts and lower-confidence contextual relations.| Subject | Predicate | Object | Confidence | Src |
|---|---|---|---|---|
| Multipole expansion | is a | mathematical series representing a function that depends on angles | 0.90 | text |
| Multipole expansion | has application | Multipole | 0.60 | section |
| Multipole expansion | has application | The | 0.60 | section |
| Multipole expansion | has application | Truncation | 0.60 | section |
| Multipole expansion | has application | Greengard | 0.60 | section |
| Multipole expansion | has application | Rokhlin | 0.60 | section |
| Multipole expansion | has application | Ewald | 0.60 | section |
| Multipole expansion | related to Expansion in spherical harmonics | Most | 0.60 | section |
| Multipole expansion | related to Expansion in spherical harmonics | Thus | 0.60 | section |
| Multipole expansion | related to Expansion in spherical harmonics | The | 0.60 | section |
| Multipole expansion | related to Expansion in spherical harmonics | Equivalently | 0.60 | section |
| Multipole expansion | related to Expansion in spherical harmonics | Here | 0.60 | section |
No triples extracted yet.
Related concept clusters Concept neighborhoods
Clusters of nearby vocabulary surrounding the topic. Scan them for adjacent concepts and language you may have missed.These clusters group vocabulary that occurs around closely connected concepts in the source material.
Connections between topic areas Semantic bridges
Bridge nodes connect otherwise separate parts of the map. Expand a row to inspect the topic groups on each side.Bridges can reveal useful research angles that are easy to miss in a flat list of related terms.
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