二元复变函数的解析性

The analyticity of double complex variables functions

由于复变函数的复杂性,很多有关复变函数的教材都重点介绍了一元复变函数的性质,简单地提及了多元复变函数,但是对多元函数的解析性,比如二元复变函数的柯西-黎曼条件,没有具体的推导.本文利用数学分析和一元复变函数的研究方法,对二元复变函数的解析性进行了讨论。

Due to the complexity of complex functions,many textbooks focus on the nature of univariate variable complex functions,but just simply mention multi-complex variables functions.However,there is no specific derivation for the analyticity of multivariate functions,such as the Cauchy Riemann condition.We will consider the analyticity of the double complex variables function.The methods of mathematical analysis and univariate variable complex functions will be applied to study the aforementioned question.