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Titlebook: Complex Analysis; In the Spirit of Lip Jane P. Gilman,Irwin Kra,Rubí E. Rodríguez Textbook 20071st edition Springer-Verlag New York 2007 Co

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Cauchy Theory: Local Behavior and Singularities of Holomorphic Functions,ions for holomorphic functions on disks. Holomorphic functions with a finite number of isolated singularities in a domain can be integrated using the ., an analog of the Cauchy Integral Formula. We discuss the local properties of these functions.
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The Fundamental Theorem in Complex Function Theory, the first section we “solve” two natural problems using complex analysis. In the second, we state the most important result in the theory of functions of one complex variable that we call the Fundamental Theorem of complex variables; its proof will occupy most of this volume.
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Power Series,troduction of new non-algebraic holomorphic functions, called elementary transcendental functions. It will turn out that allholomorphic functions are described (at least locally) by this tool. This will be proven in the next chapter.
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Cauchy Theory: Local Behavior and Singularities of Holomorphic Functions,describe a classification for isolated singularities. Functions that are holomorphic on an annulus have . expansions, an analog of power series expansions for holomorphic functions on disks. Holomorphic functions with a finite number of isolated singularities in a domain can be integrated using the
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