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Clausen's integral, sometimes called the log sine integral (Borwein and Bailey 2003, p. 88) is the n=2 case of the S_2 Clausen function Cl_2(theta) = ...

The Kronecker-Weber theorem, sometimes known as the Kronecker-Weber-Hilbert theorem, is one of the earliest known results in class field theory. In layman's terms, the ...

A rectifiable current whose boundary is also a rectifiable current.

Gelfond's theorem, also called the Gelfond-Schneider theorem, states that a^b is transcendental if 1. a is algebraic !=0,1 and 2. b is algebraic and irrational. This provides ...

If P be a point in the plane of an equilateral triangle DeltaABC, then the lengths of line segments AP, BP, and CP correspond the sides of a triangle, which is degenerate ...

The invariance of domain theorem states that if f:M->N is a one-to-one and continuous map between n-manifolds without boundary, then f is an open map.

An elliptic integral is an integral of the form int(A(x)+B(x)sqrt(S(x)))/(C(x)+D(x)sqrt(S(x)))dx, (1) or int(A(x)dx)/(B(x)sqrt(S(x))), (2) where A(x), B(x), C(x), and D(x) ...

Given a geodesic triangle (a triangle formed by the arcs of three geodesics on a smooth surface), int_(ABC)Kda=A+B+C-pi. Given the Euler characteristic chi, intintKda=2pichi, ...

A function of the coordinates which is constant along a trajectory in phase space. The number of degrees of freedom of a dynamical system such as the Duffing differential ...

int_0^inftye^(-ax)J_0(bx)dx=1/(sqrt(a^2+b^2)), where J_0(z) is the zeroth order Bessel function of the first kind.