This paper presents a detailed description of the algorithm for construction of influence (Green's) functions for a two-dimensional equation of potential over regions compound in nature. Several particular formulations are considered in the Cartesian, polar, and geographical coordinate systems. This paper also deals with an application of the Green's function method to the development of influence functions for compound multi-connected regions of complex configuration. Influence functions for appropriate simply connected regions, which have been constructed in advance, are utilized as the kernels of integral representations in the development.
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