复变函数的拟导数及哑导数

The quasi-derivative and dumb-derivative of complex variable function

利用等值原理定义了复变函数的导出函数,将导出函数由实变量延拓为复变量,利用延拓后的导出函数定义了伴随函数,利用伴随函数的偏导数定义了拟导数及哑导数,对拟导数及哑导数的存在性及具有的性质进行了研究.事实上,拟导数及哑导数就是传统所说的形式偏导数,通过研究揭示出形式偏导数不仅是形式上像偏导数,在一定意义上它是真正的偏导数,从而增进了对形式偏导数本质的理解.

The equivalent function of the complex variable function is defined by the principle of equivalence,and the equivalent function is extended from the real variable to the complex variable,the adjoint function is defined by the extended equivalent function,and the quasi-derivative and dumb-derivative are defined by the partial derivative of the adjoint function.The existence and properties of quasi-derivative and dumb-derivative are studied.In fact,the quasi-derivative and dumb-derivative are the traditional formal partial derivative.It is revealed that the formal partial derivative is not only formal like partial derivative,in a certain sense it is the true partial derivative,thus,the understanding of the essence of formal partial derivative is enhanced.