A multipole expansion is a mathematical series representing a function that depends on angles—usually the two angles used in the spherical coordinate...

recursively. The generating function approach is directly connected to the multipole expansion in electrostatics, as explained below, and is how the polynomials...

problem. It does this by expanding the system Green's function using a multipole expansion, which allows one to group sources that lie close together and treat...

mass that can exist in ideal form, but it is usually just part of a multipole expansion of a more complex structure reflecting various orders of complexity...

gamma radiation resulting from nuclear decay. Multipole radiation is analyzed using similar multipole expansion techniques that describe fields from static...

the corresponding magnetic multipole fields, and aE(l, m) and aM(l, m) are the coefficients of the expansion. The multipole fields are given by B l , m...

If the potential varies weakly over the charge distribution, the multipole expansion converges fast, so only a few first terms give an accurate approximation...

Theoretically, an electric dipole is defined by the first-order term of the multipole expansion; it consists of two equal and opposite charges that are infinitesimally...

In physics, spherical multipole moments are the coefficients in a series expansion of a potential that varies inversely with the distance R to a source...

more complete treatment may be found in pages describing multipole expansion or spherical multipole moments. (The convention in the above equations was taken...

Retrieved 2009-03-25. Fukushima, Toshio (2014). "Prolate spheroidal harmonic expansion of gravitational field". Astrophys. J. 147 (6): 152. Bibcode:2014AJ.....

dipole has a particularly simple form, and the order-1 term in the multipole expansion is precisely the point dipole field. Although there are no known...

term in the multipole expansion of electromagnetic fields besides magnetic and electric multipoles. In the electrostatic multipole expansion, all charge...

Axial multipole moments are a series expansion of the electric potential of a charge distribution localized close to the origin along one Cartesian axis...

classified by their multipolarity. There are two kinds: electric and magnetic multipole radiation. Each of these, being electromagnetic radiation, consists of...

field) of the associated adjoint bundle Monopole, the first term in a multipole expansion Monopole (wine), an appellation owned by only one winery Monopole...

charge distribution The first order term (or the second term) of the multipole expansion of a function The dielectric constant of a solvent; the measure of...

This expansion is known as the multipole expansion because the terms in this series can be regarded as energies of two interacting multipoles, one on...

consist of groups of four magnets laid out so that in the planar multipole expansion of the field, the dipole terms cancel and where the lowest significant...

these terms can be present in the multipole expansion of an electric field, for example. However, in the multipole expansion of a magnetic field, the "monopole"...

system's magnetic dipole moment, which produces the first term in the multipole expansion of a general magnetic field. Both the torque and force exerted on...

a homogeneous isotropic medium can be written as a multipole expansion. The terms in this expansion are spherical harmonics (which give the angular dependence)...

{\displaystyle \epsilon } were kept. For example calculating the multipole expansion. Griffiths, D. (1999). Introduction to Electrodynamics (Third ed...

particle centered at the cell's center of mass (or as a low-order multipole expansion). This can dramatically reduce the number of particle pair interactions...

currents involved. Conventionally, the derivation starts from a multipole expansion of the vector potential. This leads to the definition of the magnetic...

a molecule in terms of a multipole expansion around a number of centers. The idea of using a multi-center multipole expansion was earlier proposed by Robert...

when using spherical coordinates, so that a vector field admits a multipole expansion E = ∑ ℓ = 0 ∞ ∑ m = − ℓ ℓ ( E ℓ m r ( r ) Y ℓ m + E ℓ m ( 1 ) ( r...

anapole. The dynamic toroidal multipoles were theoretically introduced in the 1970s in the context of a complete multipole expansion in electrodynamics and their...

source, but external to it, can be represented by a multipole expansion. Each term in the expansion is associated with a characteristic moment and a potential...

around the microphone; formally the first-order truncation of the multipole expansion. W {\displaystyle W} (the mono signal) is the zero-order information...