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The thesis has introduced analysis function unusual matter point development history , has listed some research results of analysis function unusual matter point; The theory having introduced unusual matter point definition and the basic keeping a number , definition , fundamental character and fundamental theorem analysing them summing up the basic having summed up out several kinds isolating unusual matter point; Sum up the fundamental application having introduced a few of unusual matter point.

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In this paper, analytic functions, introduced the history of development of the singular point, analytic functions listed some of the singular point of research results; presented the definition of singular point and left the number of basic theory, a summary of the types of isolated singular point of the basic definition, analysis the nature of their basic and fundamental theorem; sum up the singular point to introduce some basic applicatio