恒等定理

设函数${\displaystyle f_{1}(z)}$和${\displaystyle f_{2}(z)}$在区域${\displaystyle D}$内解析，若${\displaystyle \{z_{n}\}\subset D}$收敛于${\displaystyle a\in D,(z_{n}\neq a)}$，且${\displaystyle f_{1}(z_{n})=f_{2}(z_{n})}$，则${\displaystyle f_{1}(z)=f_{2}(z),\forall z\in D}$[1] 。

设在区域${\displaystyle D}$内解析的函数${\displaystyle f_{1}(z)}$和${\displaystyle f_{2}(z)}$在${\displaystyle D}$内的某一子区域(或一小段弧)上相等，则它们必在区域${\displaystyle D}$内恒等。