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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) ...

A solution to the spherical Bessel differential equation. The two types of solutions are denoted j_n(x) (spherical Bessel function of the first kind) or n_n(x) (spherical ...

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 ...

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 ...

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

In particle physics, a spinor field of order 2s describes a particle of spin s, where s is an integer or half-integer. Therefore, a spinor of order 4s contains as much ...

A self-organizing data structure which uses rotations to move any accessed key to the root. This leaves recently accessed nodes near the top of the tree, making them very ...

The extension field K of a field F is called a splitting field for the polynomial f(x) in F[x] if f(x) factors completely into linear factors in K[x] and f(x) does not factor ...

In the above figure, the identical squares A, B, C appear different in width and height, because subdividing a space makes it appear larger. A different orientation can also ...