Search Results for ""

The totient function phi(n), also called Euler's totient function, is defined as the number of positive integers <=n that are relatively prime to (i.e., do not contain any ...

A function f:X->R is measurable if, for every real number a, the set {x in X:f(x)>a} is measurable. When X=R with Lebesgue measure, or more generally any Borel measure, then ...

The number of partitions of n with k or fewer addends, or equivalently, into partitions with no element greater than k. This function is denoted q(n,k) or q_k(n). (Note that ...

The j-function is the modular function defined by j(tau)=1728J(tau), (1) where tau is the half-period ratio, I[tau]>0, ...

In one dimension, the Gaussian function is the probability density function of the normal distribution, f(x)=1/(sigmasqrt(2pi))e^(-(x-mu)^2/(2sigma^2)), (1) sometimes also ...

A positive definite function f on a group G is a function for which the matrix {f(x_ix_j^(-1))} is always positive semidefinite Hermitian.

A likelihood function L(a) is the probability or probability density for the occurrence of a sample configuration x_1, ..., x_n given that the probability density f(x;a) with ...

I((chi_s^2)/(sqrt(2(k-1))),(k-3)/2)=(Gamma(1/2chi_s^2,(k-1)/2))/(Gamma((k-1)/2)), where Gamma(x) is the gamma function.

A function representable as a generalized Fourier series. Let R be a metric space with metric rho(x,y). Following Bohr (1947), a continuous function x(t) for (-infty<t<infty) ...

Given any open set U in R^n with compact closure K=U^_, there exist smooth functions which are identically one on U and vanish arbitrarily close to U. One way to express this ...