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Let f(z) be an analytic function in |z-a|<R. Then f(z)=1/(2pi)int_0^(2pi)f(z+re^(itheta))dtheta for 0<r<R.

A non-Euclidean space with constant negative Gaussian curvature.

If a sequence of double points is passed as a closed curve is traversed, each double point appears once in an even place and once in an odd place.

The Machin-like formula 1/4pi=12cot^(-1)18+8cot^(-1)57-5cot^(-1)239.

If a function phi is harmonic in a sphere, then the value of phi at the center of the sphere is the arithmetic mean of its value on the surface.

One of the quantities lambda_i appearing in the Gauss-Jacobi mechanical quadrature. They satisfy lambda_1+lambda_2+...+lambda_n = int_a^bdalpha(x) (1) = alpha(b)-alpha(a) (2) ...

For a given m, determine a complete list of fundamental binary quadratic form discriminants -d such that the class number is given by h(-d)=m. Heegner (1952) gave a solution ...

The Brent-Salamin formula, also called the Gauss-Salamin formula or Salamin formula, is a formula that uses the arithmetic-geometric mean to compute pi. It has quadratic ...

257 is a Fermat prime, and the 257-gon is therefore a constructible polygon using compass and straightedge, as proved by Gauss. An illustration of the 257-gon is not included ...

The term "integral" can refer to a number of different concepts in mathematics. The most common meaning is the the fundamenetal object of calculus corresponding to summing ...