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Let A^~, B^~, ... be operators. Then the commutator of A^~ and B^~ is defined as [A^~,B^~]=A^~B^~-B^~A^~. (1) Let a, b, ... be constants, then identities include [f(x),x] = 0 ...

A completely multiplicative function, sometimes known as linear or totally multiplicative function, is an arithmetic function f(n) such that f(mn)=f(m)f(n) holds for each ...

Let f(t) and g(t) be arbitrary functions of time t with Fourier transforms. Take f(t) = F_nu^(-1)[F(nu)](t)=int_(-infty)^inftyF(nu)e^(2piinut)dnu (1) g(t) = ...

The average number of regions into which n randomly chosen planes divide a cube is N^_(n)=1/(324)(2n+23)n(n-1)pi+n+1 (Finch 2003, p. 482). The maximum number of regions is ...

The word "degree" has many meanings in mathematics. The most common meaning is the unit of angle measure defined such that an entire rotation is 360 degrees. This unit harks ...

Let Delta_1, Delta_2, and Delta_3 be tetrahedra in projective three-space P^3. Then the tetrahedra are said to be desmically related if there exist constants alpha, beta, and ...

The angle obtained by drawing the auxiliary circle of an ellipse with center O and focus F, and drawing a line perpendicular to the semimajor axis and intersecting it at A. ...

Two quantities are said to be equal if they are, in some well-defined sense, equivalent. Equality of quantities a and b is written a=b. Equal is implemented in the Wolfram ...

The case of the Weierstrass elliptic function with invariants g_2=0 and g_3=1. The corresponding real half-period is given by omega_2 = (Gamma^3(1/3))/(4pi) (1) = ...

Let (x_1,x_2) and (y_1,y_2) be two sets of complex numbers linearly independent over the rationals. Then the four exponential conjecture posits that at least one of ...