复变函数的中值定理

证明了经典意义下的复中值定理仅对线性函数和二次多项式成立,也就是说,如果中值定理对整函数f 成立,则f 是常数、一次或二次多项式。

Mean Value Theorem for Complex Analytic Functions

In this paper,we prove that mean value theorem holds only for linear functions (including constants as a special case) and ploynominals of degree two.That is to say,If mean value theorem holds valid,in classical sense,for an entire function f ,then f must be either a constant or a polynominal of degree one or two.