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The spherical curve obtained when moving along the surface of a sphere with constant speed, while maintaining a constant angular velocity with respect to a fixed diameter ...

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 ...

Take the Helmholtz differential equation del ^2F+k^2F=0 (1) in spherical coordinates. This is just Laplace's equation in spherical coordinates with an additional term, (2) ...

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 ...

Let a spherical triangle Delta have angles A, B, and C. Then the spherical excess is given by Delta=A+B+C-pi.

The modified spherical Bessel differential equation is given by the spherical Bessel differential equation with a negative separation constant, ...

The spherical Bessel function of the second kind, denoted y_nu(z) or n_nu(z), is defined by y_nu(z)=sqrt(pi/(2z))Y_(nu+1/2)(z), (1) where Y_nu(z) is a Bessel function of the ...

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 ...

The Helmholtz differential equation in spherical coordinates is separable. In fact, it is separable under the more general condition that k^2 is of the form ...

The spherical Hankel function of the first kind h_n^((1))(z) is defined by h_n^((1))(z) = sqrt(pi/(2z))H_(n+1/2)^((1))(z) (1) = j_n(z)+in_n(z), (2) where H_n^((1))(z) is the ...