Partial and Local Argument Properties of Holomorphic and Meromorphic Complex Functions in Several Variables

The study describes a general argument analysis technique for holomorphic and meromorphic complex functions in several variables, or simply n-variable complex functions with n≥2. Argument analytic relationships for n-variable complex functions with significance similar to the argument principle for...

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Bibliographic Details
Published in:Mathematical problems in engineering Vol. 2019; no. 2019; pp. 1 - 10
Main Authors: Zhou, Jun, Duan, Zhaoxia
Format: Journal Article
Language:English
Published: Cairo, Egypt Hindawi Publishing Corporation 2019
Hindawi
John Wiley & Sons, Inc
Subjects:
Complex variables
Domains
Dynamical systems
Loci
Mathematical problems
Plotting
Systems science
Variables
ISSN:1024-123X, 1563-5147
Online Access:Get full text
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Summary:The study describes a general argument analysis technique for holomorphic and meromorphic complex functions in several variables, or simply n-variable complex functions with n≥2. Argument analytic relationships for n-variable complex functions with significance similar to the argument principle for one-variable ones are retrieved partially and locally. More precisely, argument analysis in n-variable complex functions is carried out one-by-one in terms of each and all variables, namely, partially, so that argument-principle-like relations are established in poly-disc neighborhoods of the variable domains, namely locally. The technique is applicable graphically with loci plotting, independent of Cauchy integral contour and locus orientations; it is also numerically tractable without loci plotting via argument incremental integration. Numerical examples are included to illustrate the main results.
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ISSN:1024-123X
1563-5147
DOI:10.1155/2019/7971495