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Given a series of positive terms u_i and a sequence of finite positive constants a_i, let rho=lim_(n->infty)(a_n(u_n)/(u_(n+1))-a_(n+1)). 1. If rho>0, the series converges. ...

A formal logic developed by Alonzo Church and Stephen Kleene to address the computable number problem. In the lambda calculus, lambda is defined as the abstraction operator. ...

To fit a functional form y=Ae^(Bx), (1) take the logarithm of both sides lny=lnA+Bx. (2) The best-fit values are then a = ...

Consider a collection of diagonal matrices H_1,...,H_k, which span a subspace h. Then the ith eigenvalue, i.e., the ith entry along the diagonal, is a linear functional on h, ...

A local ring is a ring R that contains a single maximal ideal. In this case, the Jacobson radical equals this maximal ideal. One property of a local ring R is that the subset ...

For a polynomial P(x_1,x_2,...,x_k), the Mahler measure of P is defined by (1) Using Jensen's formula, it can be shown that for P(x)=aproduct_(i=1)^(n)(x-alpha_i), ...

A maximum spanning tree is a spanning tree of a weighted graph having maximum weight. It can be computed by negating the weights for each edge and applying Kruskal's ...

Ore algebra is an algebra of noncommutative polynomials representing linear operators for functional equations such as linear differential or difference equations. Ore ...

The orthic inconic of a triangle is the inconic with inconic parameters x:y:z=cosA:cosB:cosC. (1) It has trilinear equation ...

The golden ratio phi can be written in terms of a nested radical in the beautiful form phi=sqrt(1+sqrt(1+sqrt(1+sqrt(1+...)))), (1) which can be written recursively as ...