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The integral representation of ln[Gamma(z)] by lnGamma(z) = int_1^zpsi_0(z^')dz^' (1) = int_0^infty[(z-1)-(1-e^(-(z-1)t))/(1-e^(-t))](e^(-t))/tdt, (2) where lnGamma(z) is the ...

A convolution is an integral that expresses the amount of overlap of one function g as it is shifted over another function f. It therefore "blends" one function with another. ...

If a complex function f is analytic in a disk contained in a simply connected domain D and f can be analytically continued along every polygonal arc in D, then f can be ...

Voronin (1975) proved the remarkable analytical property of the Riemann zeta function zeta(s) that, roughly speaking, any nonvanishing analytic function can be approximated ...

A variable with a beta binomial distribution is distributed as a binomial distribution with parameter p, where p is distribution with a beta distribution with parameters ...

The absolute moment of M_n of a probability function P(x) taken about a point a is defined by M_n=int|x-a|^nP(x)dx.

The function psi(x)={sin(x/c) |x|<cpi; 0 |x|>cpi, (1) which occurs in estimation theory.

A function is in big-theta of f if it is not much worse but also not much better than f, Theta(f(n))=O(f(n)) intersection Omega(f(n)).

A function f mapping a set X->X/R (X modulo R), where R is an equivalence relation in X, is called a canonical map.

A derivative of a complex function, which must satisfy the Cauchy-Riemann equations in order to be complex differentiable.