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A local Banach algebra is a normed algebra A=(A,|·|_A) which satisfies the following properties: 1. If x in A and f is an analytic function on a neighborhood of the spectrum ...

Following Ramanujan (1913-1914), write product_(k=1,3,5,...)^infty(1+e^(-kpisqrt(n)))=2^(1/4)e^(-pisqrt(n)/24)G_n (1) ...

Let f be analytic on the unit disk, and assume that 1. |f(z)|<=1 for all z, and 2. f(a)=b for some a,b in D(0,1), the unit disk. Then |f^'(a)|<=(1-|b|^2)/(1-|a|^2). (1) ...

A single-valued function is function that, for each point in the domain, has a unique value in the range. It is therefore one-to-one or many-to-one. A single-valued complex ...

An extended form of Bürmann's theorem. Let f(z) be a function of z analytic in a ring-shaped region A, bounded by another curve C and an inner curve c. Let theta(z) be a ...

Analytic representations the symmetric triangle wave with period 2 and varying between -1 and 1 include f(x) = 2/pisin^(-1)[sin(pix)] (1) = 1-2|1-[2(1/2x+1/4 (mod 1))]| (2) = ...

An analytic function approaches any given value arbitrarily closely in any epsilon-neighborhood of an essential singularity.

The invertible matrix theorem is a theorem in linear algebra which gives a series of equivalent conditions for an n×n square matrix A to have an inverse. In particular, A is ...

The geodesics on a general cylinder generated by lines parallel to a line l with which the tangent makes a constant angle.

A spherical image of a curve. The most common indicatrix is Dupin's indicatrix.