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An n-step Lucas sequence {L_k^((n))}_(k=1)^infty is defined by letting L_k^((n))=-1 for k<0, L_0^((n))=n, and other terms according to the linear recurrence equation ...

A theorem that can be stated either in the language of abstract algebraic curves or transcendental extensions. For an abstract algebraic curve, if x and y are nonconstant ...

A map is a way of associating unique objects to every element in a given set. So a map f:A|->B from A to B is a function f such that for every a in A, there is a unique ...

A subset E of a topological space S is said to be meager if E is of first category in S, i.e., if E can be written as the countable union of subsets which are nowhere dense ...

Polynomials m_k(x;beta,c) which form the Sheffer sequence for g(t) = ((1-c)/(1-ce^t))^beta (1) f(t) = (1-e^t)/(c^(-1)-e^t) (2) and have generating function ...

The study of the inner structure of a mathematical theory considered as a whole. It deals with the general properties of the rules according to which the objects of a certain ...

The mid-arc triangle is the triangle DeltaA^'B^'C^' whose vertices consist of the intersections of the internal angle bisectors with the incircle, where the points of ...

The radius rho of the midsphere of a polyhedron, also called the interradius. Let P be a point on the original polyhedron and P^' the corresponding point P on the dual. Then ...

Polynomials M_k(x) which form the associated Sheffer sequence for f(t)=(e^t-1)/(e^t+1) (1) and have the generating function sum_(k=0)^infty(M_k(x))/(k!)t^k=((1+t)/(1-t))^x. ...

The tensor product between modules A and B is a more general notion than the vector space tensor product. In this case, we replace "scalars" by a ring R. The familiar ...