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The Helmholtz differential equation is not separable in bispherical coordinates.

The Helmholtz differential equation is not separable in toroidal coordinates

A function S_n(z) which satisfies the recurrence relation S_(n-1)(z)-S_(n+1)(z)=2S_n^'(z) together with S_1(z)=-S_0^'(z) is called a hemicylindrical function.

A pyramidal number of the form n(n+1)(5n-2)/6, The first few are 1, 8, 26, 60, 115, ... (OEIS A002413). The generating function for the heptagonal pyramidal numbers is ...

A theorem proved by É. Cartan in 1913 which classifies the irreducible representations of complex semisimple Lie algebras.

A complex vector bundle is a vector bundle pi:E->M whose fiber bundles pi^(-1)(m) are a copy of C^k. pi is a holomorphic vector bundle if it is a holomorphic map between ...

An n-dimensional manifold M is said to be a homotopy sphere, if it is homotopy equivalent to the n-sphere S^n. Thus no homotopy group can distinguish between M and S^n. The ...

A set of graph vertices A of a graph with graph edges V is independent if it contains no graph edges.

An invertible linear transformation T:V->W is a map between vector spaces V and W with an inverse map which is also a linear transformation. When T is given by matrix ...

The commutation operation [a,b]=ab-ba corresponding to the Lie product.