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The hyperbolic volume of the knot complement of a hyperbolic knot is a knot invariant. Adams (1994) lists the hyperbolic volumes for knots and links. The hyperbolic volume of ...

A technically defined extension of the ordinary determinant to "higher dimensional" hypermatrices. Cayley (1845) originally coined the term, but subsequently used it to refer ...

A hyperfunction, discovered by Mikio Sato in 1958, is defined as a pair of holomorphic functions (f,g) which are separated by a boundary gamma. If gamma is taken to be a ...

z(1-z)(d^2y)/(dz^2)+[c-(a+b+1)z](dy)/(dz)-aby=0. It has regular singular points at 0, 1, and infty. Every second-order ordinary differential equation with at most three ...

A relation expressing a sum potentially involving binomial coefficients, factorials, rational functions, and power functions in terms of a simple result. Thanks to results by ...

A hypergeometric series sum_(k)c_k is a series for which c_0=1 and the ratio of consecutive terms is a rational function of the summation index k, i.e., one for which ...

Marsaglia (1972) has given a simple method for selecting points with a uniform distribution on the surface of a 4-sphere. This is accomplished by picking two pairs of points ...

By way of analogy with the eban numbers, iban numbers are defined as numbers whose English names do not contain the letter "i" (i.e., "i" is banned). The first few are 1, 2, ...

The (general) icosahedron is a 20-faced polyhedron (where icos- derives from the Greek word for "twenty" and -hedron comes from the Indo-European word for "seat"). Examples ...

The icosidodecadodecahedron is the uniform polyhedron with Maeder index 44 (Maeder 1997), Wenninger index 83 (Wenninger 1989), Coxeter index 56 (Coxeter et al. 1954), and ...