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Given a hypergeometric or generalized hypergeometric function _pF_q(a_1,...,a_p;b_1,...,b_q;z), the corresponding regularized hypergeometric function is defined by where ...

In the 1930s, Reidemeister first rigorously proved that knots exist which are distinct from the unknot. He did this by showing that all knot deformations can be reduced to a ...

Let a discrete distribution have probability function p_k, and let a second discrete distribution have probability function q_k. Then the relative entropy of p with respect ...

Relaxation methods are methods of solving partial differential equations that involve splitting the sparse matrix that arises from finite differencing then iterating until a ...

A surface of constant Gaussian curvature that can be given parametrically by x = a(Ucosu-U^'sinu) (1) y = -a(Usinu+U^'cosu) (2) z = v-aV^', (3) where U = ...

A real-valued univariate function f=f(x) is said to have a removable discontinuity at a point x_0 in its domain provided that both f(x_0) and lim_(x->x_0)f(x)=L<infty (1) ...

A polygon that can be dissected into n smaller copies of itself is called a rep-n-tile. The triangular polygonal spiral is also a rep-tile. The above figure shows the zeroth ...

A repeated integral is an integral taken multiple times over a single variable (as distinguished from a multiple integral, which consists of a number of integrals taken with ...

The vector space tensor product V tensor W of two group representations of a group G is also a representation of G. An element g of G acts on a basis element v tensor w by ...

The word residue is used in a number of different contexts in mathematics. Two of the most common uses are the complex residue of a pole, and the remainder of a congruence. ...