Integration in the Complex Plane

  • Ingram Bloch


In order to evaluate the intractable integrals arising from Equation 4.53, we need to devote some space first to the theory of functions of a complex variable. We shall present with no proof, or very little, many results that deserve careful study and rigorous treatment. The reader is advised to read one of the good books on the subject,1 or to attend lectures on the subject by a mathematician.


Riemann Surface Phase Angle Taylor Series Branch Point Complex Variable 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Among the well-known books on functions of a complex variable are: Churchill, R. V., J. W. Brown, and R F. Verhey. Complex Variables and Applications. New York; McGraw-Hill, 1974; Franklin, P. 3d ed. Functions of Complex Variables. Englewood Cliffs, NJ: Prentice-Hall, 1947.Google Scholar
  2. 2.
    The uniqueness of the derivative at a point must survive also the use of various complicated spirals along which h may approach zero. In fact, the C-R conditions and the continuity of the functions u and v are sufficient to guarantee uniqueness. See Churchill, R V., and J. W. Brown. Fourier Series and Boundary Value Problems 3d ed. New York: McGraw-Hill, 1978.Google Scholar

Copyright information

© Springer Science+Business Media New York 1997

Authors and Affiliations

  • Ingram Bloch

There are no affiliations available

Personalised recommendations