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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.

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