The Winding Number and the Residue Theorem

Raghavan Narasimhan and Yves Nievergelt
Additional contact information
Raghavan Narasimhan: University of Chicago, Department of Mathematics
Yves Nievergelt: Eastern Washington University, Department of Mathematics

Chapter Chapter 3 in Complex Analysis in One Variable, 2001, pp 69-85 from Springer

Abstract: Abstract The homotopy form of Cauchy’s theorem enables one to calculate many integrals of the form ∫ γ À; dz, whereÀ; is meromorphic and γ is a closed piecewise differentiable curve (it being assumed that the poles ofÀ; do not lie on Im(γ)). Formulae enabling one to do this include the so-called Cauchy formula (see §2, Theorem 2). It is, however, necessary to have some topological information about the location of the poles relative to γ. (To phrase it very vaguely, we must know how many times γ winds around a.) We begin with this topological material.

Keywords: Principal Part; Residue Theorem; Reciprocity Theorem; Laurent Expansion; Analytic Number Theory (search for similar items in EconPapers)
Date: 2001
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4612-0175-5_3

Ordering information: This item can be ordered from
http://www.springer.com/9781461201755

DOI: 10.1007/978-1-4612-0175-5_3

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().