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Consider a power series in a complex variable z g(z)=sum_(n=0)^inftya_nz^n (1) that is convergent within the open disk D:|z|<R. Convergence is limited to within D by the ...

The d-analog of a complex number s is defined as [s]_d=1-(2^d)/(s^d) (1) (Flajolet et al. 1995). For integer n, [2]!=1 and [n]_d! = [3][4]...[n] (2) = ...

A discontinuity is point at which a mathematical object is discontinuous. The left figure above illustrates a discontinuity in a one-variable function while the right figure ...

Define a Bouniakowsky polynomial as an irreducible polynomial f(x) with integer coefficients, degree >1, and GCD(f(1),f(2),...)=1. The Bouniakowsky conjecture states that ...

The Heesch number of a closed plane figure is the maximum number of times that figure can be completely surrounded by copies of itself. The determination of the maximum ...

A number (usually base 10 unless specified otherwise) which has no digitaddition generator. Such numbers were originally called Colombian numbers (S. 1974). There are ...

A series is said to be convergent if it approaches some limit (D'Angelo and West 2000, p. 259). Formally, the infinite series sum_(n=1)^(infty)a_n is convergent if the ...

If an infinite number of points in the plane are all separated by integer distances, then all the points lie on a straight line.

One of the most useful tools in nonstandard analysis is the concept of a hyperfinite set. To understand a hyperfinite set, begin with an arbitrary infinite set X whose ...

A curve created by starting with a circle, dividing it into six arcs, and flipping three alternating arcs. The process is then repeated an infinite number of times.