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The spherical harmonics Y_l^m(theta,phi) are the angular portion of the solution to Laplace's equation in spherical coordinates where azimuthal symmetry is not present. Some ...

The word "harmonic" has several distinct meanings in mathematics, none of which is obviously related to the others. Simple harmonic motion or "harmonic oscillation" refers to ...

A tensor defined in terms of the tensors which satisfy the double contraction relation.

The spherical harmonics can be generalized to vector spherical harmonics by looking for a scalar function psi and a constant vector c such that M = del x(cpsi) (1) = psi(del ...

A formula also known as the Legendre addition theorem which is derived by finding Green's functions for the spherical harmonic expansion and equating them to the generating ...

In three dimensions, the spherical harmonic differential equation is given by ...

The sum of the absolute squares of the spherical harmonics Y_l^m(theta,phi) over all values of m is sum_(m=-l)^l|Y_l^m(theta,phi)|^2=(2l+1)/(4pi). (1) The double sum over m ...

A spherical harmonic of the form sin(mphi)P_m^m(costheta) or cos(mphi)P_m^m(costheta).

A surface harmonic of degree l which is premultiplied by a factor r^l. Confusingly, solid harmonics are also known as "spherical harmonics" (Whittaker and Watson 1990, p. ...

Any linear combination of real spherical harmonics A_lP_l(costheta)+sum_(m=1)^l[A_l^mcos(mphi)+B_l^msin(mphi)]P_l^m(costheta) for l fixed whose sum is not premultiplied by a ...