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A function defined for all positive integers, sometimes also called an arithmetic function (Nagell 1951, p. 26) or number theoretic function (Wilf 1994, p. 58).

A function for which several distinct functional values correspond (as a result of different continuations) to one and the same point (Knopp 1996, p. 94).

An additive function is an arithmetic function such that whenever positive integers a and b are relatively prime, f(ab)=f(a)+f(b). An example of an additive function is ...

A function is said to be piecewise constant if it is locally constant in connected regions separated by a possibly infinite number of lower-dimensional boundaries. The ...

The triangle function is the function Lambda(x) = {0 |x|>=1; 1-|x| |x|<1 (1) = Pi(x)*Pi(x) (2) = Pi(x)*H(x+1/2)-Pi(x)*H(x-1/2), (3) where Pi(x) is the rectangle function, ...

The hazard function (also known as the failure rate, hazard rate, or force of mortality) h(x) is the ratio of the probability density function P(x) to the survival function ...

Given a subset S subset R^n and a real function f which is Gâteaux differentiable at a point x in S, f is said to be pseudoconvex at x if del f(x)·(y-x)>=0,y in ...

The Fox H-function is a very general function defined by where 0<=m<=q, 0<=n<=p, alpha_j,beta_j>0, and a_j,b_j are complex numbers such that no pole of Gamma(b_j-beta_js) for ...

A function built up of a finite combination of constant functions, field operations (addition, multiplication, division, and root extractions--the elementary operations)--and ...

The Ackermann function is the simplest example of a well-defined total function which is computable but not primitive recursive, providing a counterexample to the belief in ...