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。