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There exist a variety of formulas for either producing the nth prime as a function of n or taking on only prime values. However, all such formulas require either extremely ...

The regular tetrahedron, often simply called "the" tetrahedron, is the Platonic solid with four polyhedron vertices, six polyhedron edges, and four equivalent equilateral ...

A function f(x) is absolutely monotonic in the interval a<x<b if it has nonnegative derivatives of all orders in the region, i.e., f^((k))(x)>=0 (1) for a<x<b and k=0, 1, 2, ...

Every finite-dimensional Lie algebra of characteristic p=0 has a faithful finite-dimensional representation.

A congruence of the form f(x)=0 (mod n) where f(x) is an integer polynomial (Nagell 1951, p. 73).

The function psi(x)={sin(x/c) |x|<cpi; 0 |x|>cpi, (1) which occurs in estimation theory.

For homogeneous polynomials P and Q of degree n, [P,Q]=sum_(i_1,...,i_n>=0)(i_1!...i_n!)(a_(i,...,i_n)b_(i_1,...,i_n)).

The partial differential equation u_(xxx)-1/8u_x^3+u_x(Ae^u+Be^(-u))=0.

delta(x-t)=sum_(n=0)^inftyphi_n(x)phi_n(t), where delta(x) is the delta function.

The continuous Fourier transform is defined as f(nu) = F_t[f(t)](nu) (1) = int_(-infty)^inftyf(t)e^(-2piinut)dt. (2) Now consider generalization to the case of a discrete ...