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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 ...

Given a Jacobi theta function, the nome is defined as q(k) = e^(piitau) (1) = e^(-piK^'(k)/K(k)) (2) = e^(-piK(sqrt(1-k^2))/K(k)) (3) (Borwein and Borwein 1987, pp. 41, 109 ...

A perfect matching of a graph is a matching (i.e., an independent edge set) in which every vertex of the graph is incident to exactly one edge of the matching. A perfect ...

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 ...

An n-polyhedral graph (sometimes called a c-net) is a 3-connected simple planar graph on n nodes. Every convex polyhedron can be represented in the plane or on the surface of ...

A prime factor is a factor that is prime, i.e., one that cannot itself be factored. In general, a prime factorization takes the form ...

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

Many algorithms have been devised for determining the prime factors of a given number (a process called prime factorization). They vary quite a bit in sophistication and ...

A projective plane, sometimes called a twisted sphere (Henle 1994, p. 110), is a surface without boundary derived from a usual plane by addition of a line at infinity. Just ...

A random-connection model (RCM) is a graph-theoretic model of continuum percolation theory characterized by the existence of a stationary point process X and a non-increasing ...