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Watson (1939) considered the following three triple integrals, I_1 = 1/(pi^3)int_0^piint_0^piint_0^pi(dudvdw)/(1-cosucosvcosw) (1) = (4[K(1/2sqrt(2))]^2)/(pi^2) (2) = ...

The elastica formed by bent rods and considered in physics can be generalized to curves in a Riemannian manifold which are a critical point for ...

A sutured manifold is a tool in geometric topology which was first introduced by David Gabai in order to study taut foliations on 3-manifolds. Roughly, a sutured manifold is ...

Let [arg(f(z))] denote the change in the complex argument of a function f(z) around a contour gamma. Also let N denote the number of roots of f(z) in gamma and P denote the ...

Ball point picking is the selection of points randomly placed inside a ball. n random points can be picked in a unit ball in the Wolfram Language using the function ...

The homomorphism S which, according to the snake lemma, permits construction of an exact sequence (1) from the above commutative diagram with exact rows. The homomorphism S ...

The covariant derivative of a contravariant tensor A^a (also called the "semicolon derivative" since its symbol is a semicolon) is given by A^a_(;b) = ...

A sequent is an expression Gamma|-Lambda, where Gamma and Lambda are (possibly empty) sequences of formulas. Here, Gamma is called the antecedent and Lambda is called the ...

Let alpha, -beta, and -gamma^(-1) be the roots of the cubic equation t^3+2t^2-t-1=0, (1) then the Rogers L-function satisfies L(alpha)-L(alpha^2) = 1/7 (2) ...

The two-dimensional map x_(n+1) = [x_n+nu(1+muy_n)+epsilonnumucos(2pix_n)] (mod 1) (1) y_(n+1) = e^(-Gamma)[y_n+epsiloncos(2pix_n)], (2) where mu=(1-e^(-Gamma))/Gamma (3) ...