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A singular point a for which f(z)(z-a)^n is not differentiable for any integer n>0.

An exponent is the power p in an expression of the form a^p. The process of performing the operation of raising a base to a given power is known as exponentiation.

The partial differential equation u_t=(1+ia)u_(xx)+(1+ic)u-(1+id)|u|^2u.

Let D=D(z_0,R) be an open disk, and let u be a harmonic function on D such that u(z)>=0 for all z in D. Then for all z in D, we have 0<=u(z)<=(R/(R-|z-z_0|))^2u(z_0).

Let u_1<=u_2<=... be harmonic functions on a connected open set U subset= C. Then either u_j->infty uniformly on compact sets or there is a finite-values harmonic function u ...

A branch of topology dealing with topological invariants of manifolds.

Let a function h:U->R be continuous on an open set U subset= C. Then h is said to have the epsilon_(z_0)-property if, for each z_0 in U, there exists an epsilon_(z_0)>0 such ...

A multiple root is a root with multiplicity n>=2, also called a multiple point or repeated root. For example, in the equation (x-1)^2=0, 1 is multiple (double) root. If a ...

An algebra which does not satisfy a(bc)=(ab)c is called a nonassociative algebra.

An n-dimensional open disk of radius r is the collection of points of distance less than r from a fixed point in Euclidean n-space. Krantz (1999, p. 3) uses the symbol D(x,r) ...