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Let S(x) denote the number of positive integers not exceeding x which can be expressed as a sum of two squares (i.e., those n<=x such that the sum of squares function ...

Let K be a finite complex, let h:|K|->|K| be a continuous map. If Lambda(h)!=0, then h has a fixed point.

The length is the longest dimension of an object.

The two integrals involving Bessel functions of the first kind given by (alpha^2-beta^2)intxJ_n(alphax)J_n(betax)dx ...

The index of a vector field with finitely many zeros on a compact, oriented manifold is the same as the Euler characteristic of the manifold.

A polytope in n-dimensional Euclidean space R^n whose vertices are integer lattice points but which does not contain any other lattice points in its interior or on its ...

The volume of a prismatoid is equal to the sum of the volumes of a pyramid, a wedge, and a parallelepiped.

sum_(n=0)^(infty)(-1)^n[((2n-1)!!)/((2n)!!)]^3 = 1-(1/2)^3+((1·3)/(2·4))^3+... (1) = _3F_2(1/2,1/2,1/2; 1,1;-1) (2) = [_2F_1(1/4,1/4; 1;-1)]^2 (3) = ...

|_n]={n for n!=0; 1 for n=0. (1)

Sample size is the number of observations in a sample (Evans et al. 2000, p. 16). It is commonly denoted n or N.