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A usually simple algorithm or identity. The term is frequently applied to specific orders of Newton-Cotes formulas. The designation "rule n" is also given to the nth ...

Let the sum of squares function r_k(n) denote the number of representations of n by k squares, then the summatory function of r_2(k)/k has the asymptotic expansion ...

The conjecture that all integers >1 occur as a value of the totient valence function (i.e., all integers >1 occur as multiplicities). The conjecture was proved by Ford ...

A triangle line is a line with trilinear equation lalpha+mbeta+ngamma=0 defined relative to a reference triangle. A triangle line is called a central line iff l:m:n is a ...

Differential Equations

The circumcenter is the center O of a triangle's circumcircle. It can be found as the intersection of the perpendicular bisectors. The trilinear coordinates of the ...

The Eulerian number <n; k> gives the number of permutations of {1,2,...,n} having k permutation ascents (Graham et al. 1994, p. 267). Note that a slightly different ...

Given a triangle DeltaABC, the triangle DeltaH_AH_BH_C whose vertices are endpoints of the altitudes from each of the vertices of DeltaABC is called the orthic triangle, or ...

The summatory function Phi(n) of the totient function phi(n) is defined by Phi(n) = sum_(k=1)^(n)phi(k) (1) = sum_(m=1)^(n)msum_(d|m)(mu(d))/d (2) = ...

As a part of the study of Waring's problem, it is known that every positive integer is a sum of no more than 9 positive cubes (g(3)=9), that every "sufficiently large" ...