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Given a positive nondecreasing sequence 0<lambda_1<=lambda_2<=..., the zeta-regularized product is defined by product_(n=1)^^^inftylambda_n=exp(-zeta_lambda^'(0)), where ...

The symbol ker has at least two different meanings in mathematics. It can refer to a special function related to Bessel functions, or (written either with a capital or ...

The q-analog of the binomial theorem (1-z)^n=1-nz+(n(n-1))/(1·2)z^2-(n(n-1)(n-2))/(1·2·3)z^3+... (1) is given by (1-z/(q^n))(1-z/(q^(n-1)))...(1-z/q) ...

The van der Grinten projection is a map projection given by the transformation x = (1) y = sgn(phi)(pi|PQ-Asqrt((A^2+1)(P^2+A^2)-Q^2)|)/(P^2+A^2), (2) where A = ...

By the duality principle, for every polyhedron, there exists another polyhedron in which faces and polyhedron vertices occupy complementary locations. This polyhedron is ...

A Hadamard matrix is a type of square (-1,1)-matrix invented by Sylvester (1867) under the name of anallagmatic pavement, 26 years before Hadamard (1893) considered them. In ...

In 1611, Kepler proposed that close packing (either cubic or hexagonal close packing, both of which have maximum densities of pi/(3sqrt(2)) approx 74.048%) is the densest ...

The odd graph O_n of order n is a graph having vertices given by the (n-1)-subsets of {1,...,2n-1} such that two vertices are connected by an edge iff the associated subsets ...

The rectilinear crossing number of a graph G is the minimum number of crossings in a straight line embedding of G in a plane. It is variously denoted rcr(G), cr^_(G) ...

There are two definitions of Bernoulli polynomials in use. The nth Bernoulli polynomial is denoted here by B_n(x) (Abramowitz and Stegun 1972), and the archaic form of the ...