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

Published online by Cambridge University Press:  18 January 2021

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
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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.

Type
Research Article
Copyright
© 2021 Australian Mathematical Publishing Association Inc.

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