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A vector field is a map f:R^n|->R^n that assigns each x a vector f(x). Several vector fields are illustrated above. A vector field is uniquely specified by giving its ...

The arithmetic mean of a set of values is the quantity commonly called "the" mean or the average. Given a set of samples {x_i}, the arithmetic mean is x^_=1/Nsum_(i=1)^Nx_i. ...

A topological space X such that for every closed subset C of X and every point x in X\C, there is a continuous function f:X->[0,1] such that f(x)=0 and f(C)={1}. This is the ...

The word "graph" has (at least) two meanings in mathematics. In elementary mathematics, "graph" refers to a function graph or "graph of a function," i.e., a plot. In a ...

Polynomials s_k(x;lambda) which form a Sheffer sequence with g(t) = 1+e^(lambdat) (1) f(t) = e^t-1 (2) and have generating function ...

Orthogonal polynomials are classes of polynomials {p_n(x)} defined over a range [a,b] that obey an orthogonality relation int_a^bw(x)p_m(x)p_n(x)dx=delta_(mn)c_n, (1) where ...

The word argument is used in several differing contexts in mathematics. The most common usage refers to the argument of a function, but is also commonly used to refer to the ...

For a single variate X having a distribution P(x) with known population mean mu, the population variance var(X), commonly also written sigma^2, is defined as ...

The Bevan circle, sometimes also called the excentral circle, is the circumcircle of the excentral triangle of the reference triangle, i.e., it is the circle passing through ...

Pick two real numbers x and y at random in (0,1) with a uniform distribution. What is the probability P_(even) that [x/y], where [r] denotes the nearest integer function, is ...