A Function in the Complex Numbers is analytic on a region if it is Complex Differentiable at every point in . The terms Holomorphic Function and Regular Function are sometimes used interchangeably with ``analytic function.'' If a Function is analytic, it is infinitely Differentiable.
See also Bergman Space, Complex Differentiable, Differentiable, Pseudoanalytic Function, Semianalytic, Subanalytic
Morse, P. M. and Feshbach, H. ``Analytic Functions.'' §4.2 in
Methods of Theoretical Physics, Part I. New York: McGraw-Hill, pp. 356-374, 1953.