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The average distance between two points chosen at random inside a unit cube (the n=3 case of hypercube line picking), sometimes known as the Robbins constant, is Delta(3) = ...

Let Pi be a permutation of n elements, and let alpha_i be the number of permutation cycles of length i in this permutation. Picking Pi at random, it turns out that ...

A Hamiltonian graph, also called a Hamilton graph, is a graph possessing a Hamiltonian cycle. A graph that is not Hamiltonian is said to be nonhamiltonian. A Hamiltonian ...

The series sum_(k=1)^infty1/k (1) is called the harmonic series. It can be shown to diverge using the integral test by comparison with the function 1/x. The divergence, ...

Highly composite numbers are numbers such that divisor function d(n)=sigma_0(n) (i.e., the number of divisors of n) is greater than for any smaller n. Superabundant numbers ...

The inverse cotangent is the multivalued function cot^(-1)z (Zwillinger 1995, p. 465), also denoted arccotz (Abramowitz and Stegun 1972, p. 79; Harris and Stocker 1998, p. ...

The Jack polynomials are a family of multivariate orthogonal polynomials dependent on a positive parameter alpha. Orthogonality of the Jack polynomials is proved in Macdonald ...

The Laguerre polynomials are solutions L_n(x) to the Laguerre differential equation with nu=0. They are illustrated above for x in [0,1] and n=1, 2, ..., 5, and implemented ...

The Mangoldt function is the function defined by Lambda(n)={lnp if n=p^k for p a prime; 0 otherwise, (1) sometimes also called the lambda function. exp(Lambda(n)) has the ...

The natural logarithm of 2 is a transcendental quantity that arises often in decay problems, especially when half-lives are being converted to decay constants. ln2 has ...