Cauchy called complex variable functions that can be differentiated everywhere in the region simplex functions, and later called holomorphic functions and analytic functions. Based on this definition, B Riemann deeply studied the differential of complex variable function, and later called the above partial differential equation cauchy-riemann equations, or Cauchy-Riemann condition.
The extended data analytic function is a special complex variable function. For more than 200 years, its core theorem "Cauchy-Riemann" equations has been recognized as inseparable by the mathematical community. Wang found that although analytic function has formed a relatively perfect theory and been applied in many aspects, few phenomena in nature can meet cauchy-riemann equations's conditions, which greatly limits the application of analytic function. So I found a way to separate cauchy-riemann equations. My graduation thesis was written in 198 1, and the topic was semi-analytic function.
A series of important theorems describing the characteristics of semi-analytical functions are obtained. He has published several academic papers, such as Semi-analytic Function, Development of Semi-analytic Function, Several Theorems Equivalent to the Definition of Semi-analytic Function, Decomposition Theorem of Complex Variable Function, etc. Finally, the semi-analytical function theory was formed.
In this theory, Wang boldly separated cauchy-riemann equations's two equations, and defined the function satisfying either equation as a semi-analytical function, thus realizing the popularization of analytical functions and providing a general method for studying general functions that cannot be solved by analytical functions.
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