Integral Calculus in the Complex Plane C

  • Eberhard FreitagEmail author
  • Rolf Busam
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.


Complex Plane Entire Function Star Center Leibniz Rule Elementary Domain 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  1. 1.Universität HeidelbergInst. MathematikGermany

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