# spherical harmonics

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## spherical harmonics

[′sfir·ə·kəl här′män·iks]
(mathematics)
Solutions of Laplace's equation in spherical coordinates.
References in periodicals archive ?
it is possible to express the ODF f in a (generally infinite) sum of 'spherical harmonics', where the spherical harmonics are the two-dimensional analogues to the sines and cosines in the Fourier series (see Section 2).
The ellipsoidal harmonics in these spheroconical coordinates replace the spherical harmonics of spherical polar coordinates.
Among their topics are summaries of finite difference method and pseudospectral methods, global Radial basis functions for solving partial differential equations, applications to geo-modeling in spherical domains, spherical harmonics, and some node distribution strategies.
n] is the Laplace spherical harmonics of the gravity anomaly calculated from the GGM of degree n, M is the maximum degree of GGM, [b.
Model for the cube when the number of spherical harmonics is 9: a--cube drawing; b--spherical harmonics of the equation for the cube surface
Spherical harmonics and basic coupling coefficients for the group SO(5) in an SO(3) basis.
Due to the orthogonality of the vector spherical harmonics and the expansion of the Green dyadic, Eq.
MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] are the spherical delta functions (see [2, 8, 9]) and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] are the vector spherical harmonics ([10]).
n] of spherical harmonics and from a set of the least-squares modification parameters {[b.
This edition has a new chapter on complex variable methods and new sections on Cauchy-Euler equations, Bessel functions, Legendre polynomials, spherical harmonics, applications of Fourier transformations, and general hyperbolic equations.
Here, we use some general properties of spherical harmonics [9] to deal with all dimensions d.

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