Analytic Function

A Function in the Complex Numbers $\Bbb{C}$ is analytic on a region $R$ if it is Complex Differentiable at every point in $R$. 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

References

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.