Multipole Expansion

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High Quality Content by WIKIPEDIA articles! multipole expansion is a mathematical series representing a function that depends on angles usually the two angles on a sphere. These series are useful because they can often be truncated, meaning that only the first few terms need to be retained for a good approximation to the original function. The function being expanded may be complex in general. Multipole expansions are very frequently used in the study of electromagnetic, and gravitational fields, where the fields at distant points are given in terms of sources in a small region. The multipole expansion with angles is often combined with an expansion in radius. Such a combination gives an expansion describing a function throughout three-dimensional space. The multipole expansion is expressed as a sum of terms with progressively finer angular features. For example, the initial term called the zero-th, or monopole, moment is a constant, independent of angle. The following term the first, or dipole, moment varies once from positive to negative around the sphere. Higher-order terms (like the quadrupole and octupole) vary more quickly with angles.

Weitere Informationen

  • Allgemeine Informationen
    • GTIN 09786130241247
    • Editor Frederic P. Miller, Agnes F. Vandome, John McBrewster
    • Sprache Englisch
    • Größe H220mm x B150mm x T10mm
    • Jahr 2009
    • EAN 9786130241247
    • Format Fachbuch
    • ISBN 978-613-0-24124-7
    • Titel Multipole Expansion
    • Untertitel Series (mathematics), Function (mathematics), Spherical coordinate system, Complex number, Electromagnetic field, Gravitational field, Moment (mathematics), Dipole, Quadrupole, Spherical harmonics
    • Gewicht 272g
    • Herausgeber Alphascript Publishing
    • Anzahl Seiten 172
    • Genre Mathematik

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