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A VARIANT OF CAUCHY’S ARGUMENT PRINCIPLE FOR ANALYTIC FUNCTIONS WHICH APPLIES TO CURVES CONTAINING ZEROS

Part of: Miscellaneous topics of analysis in the complex domain

Published online by Cambridge University Press:  18 January 2021

MAHER BOUDABRA Open the ORCID record for MAHER BOUDABRA [Opens in a new window]  and
GREG MARKOWSKY Open the ORCID record for GREG MARKOWSKY [Opens in a new window]
MAHER BOUDABRA*
Affiliation:
School of Mathematics, Monash University, Clayton, Victoria3800, Australia
GREG MARKOWSKY
Affiliation:
School of Mathematics, Monash University, Clayton, Victoria3800, Australia e-mail: gmarkowsky@gmail.com
*
e-mail: maher.boudabra@monash.edu
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Abstract

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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.

Keywords

Cauchy’s argument principlewinding number

MSC classification

Primary: 30E20: Integration, integrals of Cauchy type, integral representations of analytic functions
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 103 , Issue 3 , June 2021 , pp. 486 - 492
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Copyright
© 2021 Australian Mathematical Publishing Association Inc.

References

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