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Origin and Applications of the Theory 1 The development of the idea of analytic functions
The usefulness of the theory
Founders of the theory
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a+ib absolute value algebraic amplitude analytic continuation analytic functions analytic throughout angle approach zero becomes infinite boundary branch branch-point Burkhardt-Rasor Cauchy-Riemann equations Cauchy's integral theorem Chapter circle of convergence closed curve co-ordinates coefficients complex numbers complex variable conformal mapping constant continuous function corresponding curve integral curve segment defined definite integral definition differential equations equal essential singular point example expression finite number foregoing formula func given Goursat-Hedrick Hence indefinite integral initial point integral linear transformation interior isogonal Laurent's series limit linear transformation logarithmic loop lytic many-valued functions mathematical monodromic group negative obtain origin Osgood partial derivatives path Pierpont point z0 polynomial positive power series real functions real number real variable Riemann surface root series converges similarly simply connected simply connected region single-valued and analytic solution Taylor's series theory of functions throughout a neighborhood throughout a region tion tive uniformly convergent vanish x+iy z-plane z-point