region of holomorphy

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Holomorphic function — A rectangular grid (top) and its image under a holomorphic function f (bottom). In mathematics, holomorphic functions are the central objects of study in complex analysis. A holomorphic function is a complex valued function of one or more complex … Wikipedia
Analytic continuation — In complex analysis, a branch of mathematics, analytic continuation is a technique to extend the domain of a given analytic function. Analytic continuation often succeeds in defining further values of a function, for example in a new region where … Wikipedia
Morera's theorem — If the integral along every C is zero, then ƒ is holomorphic on D. In complex analysis, a branch of mathematics, Morera s theorem, named after Giacinto Morera, gives an important criterion for proving that a function is holomorphic. Morera s… … Wikipedia
Mittag-Leffler star — Illustration of the Mittag Leffler star (the region bounded by the blue contour). The original disk U is centered at a. In complex analysis, a branch of mathematics, the Mittag Leffler star of a complex analytic function is a set in the… … Wikipedia

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