An analytic function is a complex function that is complex differentiable at every point in a region.

A complex function is said to be analytic on a region R if it is complex differentiable at every point in R. The terms holomorphic function, differentiable function, and complex differentiable function are sometimes used interchangeably with "analytic function". Many mathematicians prefer the term "holomorphic function" (or "holomorphic map") to "analytic function", while "analytic" appears to be in widespread use among physicists, engineers, and in some older texts (e.g., Morse and Feshbach 1953, pp. 356-374; Knopp 1996, pp. 83-111, p. 83).

anti-analytic function | Bergman space | Cauchy-Riemann equations | complex differentiable | complex function | complex plane | differentiable | entire function | holomorphic function | meromorphic function | pseudoanalytic function | real analytic function | regular function | semianalytic | singularity | subanalytic

college level