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The number of alternating permutations for n elements is sometimes called an Euler zigzag number. Denote the number of alternating permutations on n elements for which the ...

Let f(x,y) be a homogeneous function of order n so that f(tx,ty)=t^nf(x,y). (1) Then define x^'=xt and y^'=yt. Then nt^(n-1)f(x,y) = ...

An event is a certain subset of a probability space. Events are therefore collections of outcomes on which probabilities have been assigned. Events are sometimes assumed to ...

An experiment E(S,F,P) is defined (Papoulis 1984, p. 30) as a mathematical object consisting of the following elements. 1. A set S (the probability space) of elements. 2. A ...

The extended complex plane is the name given to the complex plane with a point at infinity attached: C union {infty^~}, where infty^~ denotes complex infinity. It is also ...

An entire function f is said to be of finite order if there exist numbers a,r>0 such that |f(z)|<=exp(|z|^a) for all |z|>r. The infimum of all numbers a for which this ...

A closed embedded smooth plane curve has at least four vertices, where a vertex is defined as an extremum of curvature.

A function element is an ordered pair (f,U) where U is a disk D(Z_0,r) and f is an analytic function defined on U. If W is an open set, then a function element in W is a pair ...

The infimum of all number a for which |f(z)|<=exp(|z|^a) holds for all |z|>r and f an entire function, is called the order of f, denoted lambda=lambda(f) (Krantz 1999, p. ...

A unit of angular measure in which the angle of an entire circle is 400 gradians. A right angle is therefore 100 gradians. A gradian is sometimes also called a gon or a grade.