The (complex-valued) function E(eitX), where X is a random variable, t is a real variable and . If X is continuous and has probability density function f then the characteristic function is a multiple of the Fourier transform of f. The characteristic function is closely related to the moment-generating function and has the advantage of always existing. The first English use of the phrase ‘characteristic function’ was by Kullback in 1934.
Computer
of a subset S of a universal set U. A function that indicates whether or not an element is a member of the subset S. It is the function
defined as follows:The codomain might also be given as {true,false} or {1,2}.