Non-Integer Valued Winding Numbers and a Generalized Residue Theorem
Joint Authors
Hungerbühler, Norbert
Wasem, Micha
Source
Issue
Vol. 2019, Issue 2019 (31 Dec. 2019), pp.1-9, 9 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2019-03-11
Country of Publication
Egypt
No. of Pages
9
Main Subjects
Abstract EN
We define a generalization of the winding number of a piecewise C 1 cycle in the complex plane which has a geometric meaning also for points which lie on the cycle.
The computation of this winding number relies on the Cauchy principal value but is also possible in a real version via an integral with bounded integrand.
The new winding number allows to establish a generalized residue theorem which covers also the situation where singularities lie on the cycle.
This residue theorem can be used to calculate the value of improper integrals for which the standard technique with the classical residue theorem does not apply.
American Psychological Association (APA)
Hungerbühler, Norbert& Wasem, Micha. 2019. Non-Integer Valued Winding Numbers and a Generalized Residue Theorem. Journal of Mathematics،Vol. 2019, no. 2019, pp.1-9.
https://search.emarefa.net/detail/BIM-1181393
Modern Language Association (MLA)
Hungerbühler, Norbert& Wasem, Micha. Non-Integer Valued Winding Numbers and a Generalized Residue Theorem. Journal of Mathematics No. 2019 (2019), pp.1-9.
https://search.emarefa.net/detail/BIM-1181393
American Medical Association (AMA)
Hungerbühler, Norbert& Wasem, Micha. Non-Integer Valued Winding Numbers and a Generalized Residue Theorem. Journal of Mathematics. 2019. Vol. 2019, no. 2019, pp.1-9.
https://search.emarefa.net/detail/BIM-1181393
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1181393