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Why is it called analytic function? What does analysis mean in mathematics here? Why not call it a complex variable function that can be differentiated everywhere?
Analytic function is a complex function, which can be derived anywhere in a region. /kloc-in the 7th century, L. Euler and J.leR. D'Alembert found that the potential function φ (x, y) and the flow function ψ (x, y) of the irrotational field of plane incompressible fluid have continuous partial derivatives and satisfy the differential equation, and pointed out that f (z) = φ (x, y)+i ψ.

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.

Baidu Encyclopedia-Analysis Function