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An integer is k-smooth if it has no prime factors >k. The following table gives the first few k-smooth numbers for small k. Berndt (1994, p. 52) called the 7-smooth numbers ...

A tensor t is said to satisfy the double contraction relation when t_(ij)^m^_t_(ij)^n=delta_(mn). (1) This equation is satisfied by t^^^0 = (2z^^z^^-x^^x^^-y^^y^^)/(sqrt(6)) ...

A hexagrammic prism is a prism formed by two regular hexagrams offset along their symmetry axis and with corresponding edges connected by lateral faces. For an equilateral ...

An n×n array of the integers from 1 to n^2 such that the difference between any one integer and its neighbor (horizontally, vertically, or diagonally, without wrapping ...

The number of ways a set of n elements can be partitioned into nonempty subsets is called a Bell number and is denoted B_n (not to be confused with the Bernoulli number, ...

The third singular value k_3, corresponding to K^'(k_3)=sqrt(3)K(k_3), (1) is given by k_3=sin(pi/(12))=1/4(sqrt(6)-sqrt(2)). (2) As shown by Legendre, ...

Gamma functions of argument 2z can be expressed in terms of gamma functions of smaller arguments. From the definition of the beta function, ...

The Dedekind eta function is defined over the upper half-plane H={tau:I[tau]>0} by eta(tau) = q^_^(1/24)(q^_)_infty (1) = q^_^(1/24)product_(k=1)^(infty)(1-q^_^k) (2) = ...

An orthogonal coordinate system is a system of curvilinear coordinates in which each family of surfaces intersects the others at right angles. Orthogonal coordinates ...

A nexus number is a figurate number built up of the nexus of cells less than n steps away from a given cell. The nth d-dimensional nexus number is given by N_d(n) = ...