Global analytic function

In the mathematical field of complex analysis, a global analytic function (or complete analytic function) is a generalization of the notion of an analytic function which allows for functions to have multiple branches. Global analytic functions arise naturally in considering the possible analytic continuations of an analytic function, since analytic continuations may have a non-trivial monodromy. They are one foundation for the theory of Riemann surfaces.

The definition of a global analytic function goes back to Karl Weierstrass.

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