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The operator representing the computation of a derivative, D^~=d/(dx), (1) sometimes also called the Newton-Leibniz operator. The second derivative is then denoted D^~^2, the ...

An algorithm which allows digits of a given number to be calculated without requiring the computation of earlier digits. The BBP formula for pi is the best-known such ...

Consider the process of taking a number, taking its digit sum, then adding the digits of numbers derived from it, etc., until the remaining number has only one digit. The ...

A local sink is a node of a directed graph with no exiting edges, also called a terminal (Borowski and Borwein 1991, p. 401; left figure). A global sink (often simply called ...

An unlabeled transitive digraph with n nodes is called a "topology." The numbers of distinct topologies on n=1, 2, ... nodes are 1, 3, 9, 33, 139, 718, 4535, ... (OEIS ...

The dihedral group D_6 gives the group of symmetries of a regular hexagon. The group generators are given by a counterclockwise rotation through pi/3 radians and reflection ...

A number n such that the "LED representation" of n (i.e., the arrangement of horizonal and vertical lines seen on a digital clock or pocket calculator), n upside down, n in a ...

sum_(1<=k<=n)(n; k)((-1)^(k-1))/(k^m)=sum_(1<=i_1<=i_2<=...<=i_m<=n)1/(i_1i_2...i_m), (1) where (n; k) is a binomial coefficient (Dilcher 1995, Flajolet and Sedgewick 1995, ...

The partial order width of a set P is equal to the minimum number of chains needed to cover P. Equivalently, if a set P of ab+1 elements is partially ordered, then P contains ...

Dini's theorem is a result in real analysis relating pointwise convergence of sequences of functions to uniform convergence on a closed interval. For an increasing sequence ...