摘要
给出了方程f(z^2)=F(f(z))与方程f(2z)=F(f(z))的整函数解之间的关系,并对方程f(z^2)=F(f(z))的非常数整函数解的性质以及特殊情形的整函数解进行了讨论。
This paper studies the solutions of the functional equation f(z^2) = F(fz)). First the relation between the solutions of the equation f(z^2)=F(f(z)) and f(2z)=F(fz)) is shown. Then, the properties of the solutions of equation f(z^2) = F(fz)) are given. Moreover, if F(z) is a polynomial of order 2, the solution of the equation f(z^2) = F(fz)) can be explieitly given.
关键词
整函数
超越整函数
函数方程
Entire function, Entire transcendental function, Order of entire function
