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Integral Calculus in the Complex Plane C

  • Eberhard FreitagEmail author
  • Rolf Busam
Chapter
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Part of the Universitext book series (UTX)

In Section I.5 we already encountered the problem of finding a primitive function for a given analytic function \(f:D \to \mathcal{C}, D\subset \mathcal{C}\) open, i. e., an analytic function \(F:D\to \mathcal{C}\) such that \(F^\prime = f.\)

In general, one may ask: Which functions \(f : D \to \mathcal{C}, D \subset \mathcal{C}\) open, have a primitive? Recall that in the real case any continuous function \(f : [a, b] \to \mathcal{R}, a < b\), has a primitive, namely, for example the integral
$$F(x): = \int^{x}_{a} f(t) dt.$$
Whether one uses the notion of a RIEMANN integral or the integral for regulated functions is irrelevant in this connection.

Keywords

Complex Plane Entire Function Star Center Leibniz Rule Elementary Domain 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  1. 1.Universität HeidelbergInst. MathematikGermany

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