Chapter 4. Calculus of Residues

  1. Prof. Dr. Charlie Harper

Published Online: 28 JAN 2005

DOI: 10.1002/3527603077.ch4

Analytic Methods in Physics

Analytic Methods in Physics

How to Cite

Harper, C. (1999) Calculus of Residues, in Analytic Methods in Physics, Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim, FRG. doi: 10.1002/3527603077.ch4

Author Information

  1. California State University, Hayward, USA

Publication History

  1. Published Online: 28 JAN 2005
  2. Published Print: 12 OCT 1999

ISBN Information

Print ISBN: 9783527402168

Online ISBN: 9783527603077

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Keywords:

  • residues;
  • singular points;
  • Cauchy residue theorem;
  • Cauchy principal value;
  • definite integrals;
  • dispersion relations

Summary

This chapter contains sections titled:

  • Isolated Singular Points

  • Evaluation of Residues

    • m-th-Order Pole

    • Simple Pole

  • The Cauchy Residue Theorem

  • The Cauchy Principal Value

  • Evaluation of Definite Integrals

    • Integrals of the Form equation image

    • Integrals of the Form equation image

    • A Digression on Jordan's Lemma

    • Integrals of the Form equation image

  • Dispersion Relations

  • Conformal Transformations

  • Multi-valued Functions

  • Problems