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A pairing function is a function that reversibly maps Z^*×Z^* onto Z^*, where Z^*={0,1,2,...} denotes nonnegative integers. Pairing functions arise naturally in the ...

The parabolic cylinder functions are a class of functions sometimes called Weber functions. There are a number of slightly different definitions in use by various authors. ...

The dual of Brianchon's theorem (Casey 1888, p. 146), discovered by B. Pascal in 1640 when he was just 16 years old (Leibniz 1640; Wells 1986, p. 69). It states that, given a ...

The beautiful arrangement of leaves in some plants, called phyllotaxis, obeys a number of subtle mathematical relationships. For instance, the florets in the head of a ...

The Pochhammer symbol (x)_n = (Gamma(x+n))/(Gamma(x)) (1) = x(x+1)...(x+n-1) (2) (Abramowitz and Stegun 1972, p. 256; Spanier 1987; Koepf 1998, p. 5) for n>=0 is an ...

The factorization of a number into its constituent primes, also called prime decomposition. Given a positive integer n>=2, the prime factorization is written ...

A quadratic map is a quadratic recurrence equation of the form x_(n+1)=a_2x_n^2+a_1x_n+a_0. (1) While some quadratic maps are solvable in closed form (for example, the three ...

A set is a finite or infinite collection of objects in which order has no significance, and multiplicity is generally also ignored (unlike a list or multiset). Members of a ...

The symmetric group S_n of degree n is the group of all permutations on n symbols. S_n is therefore a permutation group of order n! and contains as subgroups every group of ...

Thurston's conjecture proposed a complete characterization of geometric structures on three-dimensional manifolds. Before stating Thurston's geometrization conjecture in ...