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An Abelian group is a group for which the elements commute (i.e., AB=BA for all elements A and B). Abelian groups therefore correspond to groups with symmetric multiplication ...

The Barnes G-function is an analytic continuation of the G-function defined in the construction of the Glaisher-Kinkelin constant G(n)=([Gamma(n)]^(n-1))/(H(n-1)) (1) for ...

666 is the occult "number of the beast," also called the "sign of the devil" (Wang 1994), associated in the Bible with the Antichrist. It has figured in many numerological ...

A phenomenological law also called the first digit law, first digit phenomenon, or leading digit phenomenon. Benford's law states that in listings, tables of statistics, ...

The base 2 method of counting in which only the digits 0 and 1 are used. In this base, the number 1011 equals 1·2^0+1·2^1+0·2^2+1·2^3=11. This base is used in computers, ...

Consider the probability Q_1(n,d) that no two people out of a group of n will have matching birthdays out of d equally possible birthdays. Start with an arbitrary person's ...

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!! ...

Given a circle expressed in trilinear coordinates by a central circle is a circle such that l:m:n is a triangle center and k is a homogeneous function that is symmetric in ...

Consecutive number sequences are sequences constructed by concatenating numbers of a given type. Many of these sequences were considered by Smarandache and so are sometimes ...

Scan the decimal expansion of a constant (including any digits to the left of the decimal point) until all n-digit strings have been seen (including 0-padded strings). The ...