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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 ...

Given a Poisson process, the probability of obtaining exactly n successes in N trials is given by the limit of a binomial distribution P_p(n|N)=(N!)/(n!(N-n)!)p^n(1-p)^(N-n). ...

Square triangle picking is the selection of triples of points (corresponding to endpoints of a triangle) randomly placed inside a square. n random triangles can be picked in ...

The point of concurrence K of the symmedians, sometimes also called the Lemoine point (in England and France) or the Grebe point (in Germany). Equivalently, the symmedian ...

Probability and Statistics

The cube is the Platonic solid composed of six square faces that meet each other at right angles and has eight vertices and 12 edges. It is also the uniform polyhedron with ...

The constant e is base of the natural logarithm. e is sometimes known as Napier's constant, although its symbol (e) honors Euler. e is the unique number with the property ...

The (complete) gamma function Gamma(n) is defined to be an extension of the factorial to complex and real number arguments. It is related to the factorial by Gamma(n)=(n-1)!, ...

The inverse tangent is the multivalued function tan^(-1)z (Zwillinger 1995, p. 465), also denoted arctanz (Abramowitz and Stegun 1972, p. 79; Harris and Stocker 1998, p. 311; ...

The power tower of order k is defined as a^^k=a^(a^(·^(·^(·^a))))_()_(k), (1) where ^ is Knuth up-arrow notation (Knuth 1976), which in turn is defined by ...