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

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  • Jun Zhou
  • Zhaoxia Duan

Abstract

The study describes a general argument analysis technique for holomorphic and meromorphic complex functions in several variables, or simply - variable complex functions with . Argument analytic relationships for - variable complex functions with significance similar to the argument principle for one-variable ones are retrieved partially and locally. More precisely, argument analysis in - 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.

Suggested Citation

  • Jun Zhou & Zhaoxia Duan, 2019. "Partial and Local Argument Properties of Holomorphic and Meromorphic Complex Functions in Several Variables," Mathematical Problems in Engineering, Hindawi, vol. 2019, pages 1-10, August.
    • Handle: RePEc:hin:jnlmpe:7971495
    DOI: 10.1155/2019/7971495
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