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Montgomery's pair correlation conjecture, published in 1973, asserts that the two-point correlation function R_2(r) for the zeros of the Riemann zeta function zeta(z) on the ...

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 ...

Let a discrete distribution have probability function p_k, and let a second discrete distribution have probability function q_k. Then the relative entropy of p with respect ...

Given two distributions Y and X with joint probability density function f(x,y), let U=Y/X be the ratio distribution. Then the distribution function of u is D(u) = P(U<=u) (1) ...

The triangular distribution is a continuous distribution defined on the range x in [a,b] with probability density function P(x)={(2(x-a))/((b-a)(c-a)) for a<=x<=c; ...

The Gudermannian function is the odd function denoted either gamma(x) or gd(x) which arises in the inverse equations for the Mercator projection. phi(y)=gd(y) expresses the ...

The principal branch of an analytic multivalued function, also called a principal sheet, is a single-valued "slice" (i.e., branch) of the function chosen that is for ...

A class of formal series expansions in derivatives of a distribution Psi(t) which may (but need not) be the normal distribution function Phi(t)=1/(sqrt(2pi))e^(-t^2/2) (1) ...

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)).