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The logarithmic integral (in the "American" convention; Abramowitz and Stegun 1972; Edwards 2001, p. 26), is defined for real x as li(x) = {int_0^x(dt)/(lnt) for 0<x<1; ...
The natural logarithm lnx is the logarithm having base e, where e=2.718281828.... (1) This function can be defined lnx=int_1^x(dt)/t (2) for x>0. This definition means that e ...
The incenter I is the center of the incircle for a polygon or insphere for a polyhedron (when they exist). The corresponding radius of the incircle or insphere is known as ...
The nth central binomial coefficient is defined as (2n; n) = ((2n)!)/((n!)^2) (1) = (2^n(2n-1)!!)/(n!), (2) where (n; k) is a binomial coefficient, n! is a factorial, and n!! ...
Zero is the integer denoted 0 that, when used as a counting number, means that no objects are present. It is the only integer (and, in fact, the only real number) that is ...
The important binomial theorem states that sum_(k=0)^n(n; k)r^k=(1+r)^n. (1) Consider sums of powers of binomial coefficients a_n^((r)) = sum_(k=0)^(n)(n; k)^r (2) = ...
The Euler-Maclaurin integration and sums formulas can be derived from Darboux's formula by substituting the Bernoulli polynomial B_n(t) in for the function phi(t). ...
Wirsing (1974) showed, among other results, that if F_n(x) is the Gauss-Kuzmin distribution, then lim_(n->infty)(F_n(x)-lg(1+x))/((-lambda)^n)=Psi(x), (1) where ...
A genetic algorithm is a class of adaptive stochastic optimization algorithms involving search and optimization. Genetic algorithms were first used by Holland (1975). The ...
The Hilbert curve is a Lindenmayer system invented by Hilbert (1891) whose limit is a plane-filling function which fills a square. Traversing the polyhedron vertices of an ...
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