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The central binomial coefficient (2n; n) is never squarefree for n>4. This was proved true for all sufficiently large n by Sárkőzy's theorem. Goetgheluck (1988) proved the ...

erf(z) is the "error function" encountered in integrating the normal distribution (which is a normalized form of the Gaussian function). It is an entire function defined by ...

Erfc is the complementary error function, commonly denoted erfc(z), is an entire function defined by erfc(z) = 1-erf(z) (1) = 2/(sqrt(pi))int_z^inftye^(-t^2)dt. (2) It is ...

The second-order ordinary differential equation y^('')+2xy^'-2ny=0, (1) whose solutions may be written either y=Aerfc_n(x)+Berfc_n(-x), (2) where erfc_n(x) is the repeated ...

The "imaginary error function" erfi(z) is an entire function defined by erfi(z)=-ierf(iz), (1) where erf(z) is the erf function. It is implemented in the Wolfram Language as ...

An endomorphism is called ergodic if it is true that T^(-1)A=A implies m(A)=0 or 1, where T^(-1)A={x in X:T(x) in A}. Examples of ergodic endomorphisms include the map X->2x ...

Ergodic theory can be described as the statistical and qualitative behavior of measurable group and semigroup actions on measure spaces. The group is most commonly N, R, R-+, ...

A transformation which has only trivial invariant subsets is said to be ergodic.

Given a Poisson distribution with a rate of change lambda, the distribution function D(x) giving the waiting times until the hth Poisson event is D(x) = ...

A program initiated by F. Klein in an 1872 lecture to describe geometric structures in terms of their automorphism groups.