Titlebook: Complex Analysis; Serge Lang Textbook 1999Latest edition Springer Science+Business Media New York 1999 Cauchy‘s integral formula.Complex a

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Complex Numbers and Functionse rational numbers have a solution in real numbers. For instance, .. = 2 is such an equation. However, we also know some equations having no solution in real numbers, for instance .. = −1, or .. = −2. We define a new kind of number where such equations have solutions. The new kind of numbers will be called . numbers.

GLIB

Schwarz Reflection on . ⋃ .. The process of extending . in this way is called .. If ., . are connected, and have in common an infinite set of points which have a point of accumulation in ., then an analytic continuation of . to . is uniquely determined. Indeed, if . analytic on . and . on ., then . the only such function by Theorem 1.2 of Chapter III.

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Graduate Texts in Mathematicshttp://image.papertrans.cn/c/image/231354.jpg

LIMIT

Perspektiven der Kognitiven Linguistik,e rational numbers have a solution in real numbers. For instance, .. = 2 is such an equation. However, we also know some equations having no solution in real numbers, for instance .. = −1, or .. = −2. We define a new kind of number where such equations have solutions. The new kind of numbers will be

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Ist das nicht alles das Gleiche?,rincipal ways will be by means of power series. Thus we shall see that the series . converges for all . to define a function which is equal to ... Similarly, we shall extend the values of sin . and cos . by their usual series to complex valued functions of a complex variable, and we shall see that t

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https://doi.org/10.1007/978-3-658-28341-4perties of paths: (1) properties of homotopy, and (2) properties having to do with integration, relating to the number of times a curve “winds” around a point, as we already saw when we evaluated the integral.along a circle centered at .. These properties are of course related, but they also exist i