A Variant of Cauchy's Argument Principle for Analytic Functions Which Applies to Curves Containing Zeros

Maher Boudabra; Greg Markowsky

doi:10.1017/S0004972720001458

A Variant of Cauchy's Argument Principle for Analytic Functions Which Applies to Curves Containing Zeros

Maher Boudabra^*
, Greg Markowsky

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

Abstract

The standard version of Cauchy's argument principle, applied to a holomorphic function f, requires that f has no zeros on the curve of integration. In this note, we give a generalisation of such a principle which covers the case when f has zeros on the curve, as well as an application.

Original language	English
Pages (from-to)	486-492
Number of pages	7
Journal	Bulletin of the Australian Mathematical Society
Volume	103
Issue number	3
DOIs	https://doi.org/10.1017/S0004972720001458
State	Published - Jun 2021
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2021 Australian Mathematical Publishing Association Inc.

Keywords

Cauchy's argument principle
winding number

ASJC Scopus subject areas

General Mathematics

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10.1017/S0004972720001458

Cite this

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title = "A Variant of Cauchy's Argument Principle for Analytic Functions Which Applies to Curves Containing Zeros",

abstract = "The standard version of Cauchy's argument principle, applied to a holomorphic function f, requires that f has no zeros on the curve of integration. In this note, we give a generalisation of such a principle which covers the case when f has zeros on the curve, as well as an application.",

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author = "Maher Boudabra and Greg Markowsky",

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year = "2021",

month = jun,

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language = "English",

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AB - The standard version of Cauchy's argument principle, applied to a holomorphic function f, requires that f has no zeros on the curve of integration. In this note, we give a generalisation of such a principle which covers the case when f has zeros on the curve, as well as an application.

KW - Cauchy's argument principle

KW - winding number

UR - https://www.scopus.com/pages/publications/85099731428

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DO - 10.1017/S0004972720001458

M3 - Article

AN - SCOPUS:85099731428

SN - 0004-9727

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ER -

A Variant of Cauchy's Argument Principle for Analytic Functions Which Applies to Curves Containing Zeros

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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Cite this