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An alternating knot is a knot which possesses a knot diagram in which crossings alternate between under- and overpasses. Not all knot diagrams of alternating knots need be ...

The beta function B(p,q) is the name used by Legendre and Whittaker and Watson (1990) for the beta integral (also called the Eulerian integral of the first kind). It is ...

A Boolean algebra is a mathematical structure that is similar to a Boolean ring, but that is defined using the meet and join operators instead of the usual addition and ...

In common usage, a cardinal number is a number used in counting (a counting number), such as 1, 2, 3, .... In formal set theory, a cardinal number (also called "the ...

The two functions theta(x) and psi(x) defined below are known as the Chebyshev functions. The function theta(x) is defined by theta(x) = sum_(k=1)^(pi(x))lnp_k (1) = ...

The term "cylinder" has a number of related meanings. In its most general usage, the word "cylinder" refers to a solid bounded by a closed generalized cylinder (a.k.a. ...

When the elliptic modulus k has a singular value, the complete elliptic integrals may be computed in analytic form in terms of gamma functions. Abel (quoted in Whittaker and ...

An n-step Fibonacci sequence {F_k^((n))}_(k=1)^infty is defined by letting F_k^((n))=0 for k<=0, F_1^((n))=F_2^((n))=1, and other terms according to the linear recurrence ...

The Cartesian graph product G=G_1 square G_2, also called the graph box product and sometimes simply known as "the" graph product (Beineke and Wilson 2004, p. 104) and ...

An inner product is a generalization of the dot product. In a vector space, it is a way to multiply vectors together, with the result of this multiplication being a scalar. ...