关于解析延拓的一种方法

One Method of Analysis of Continuation

设f(z)=∑∞n=1anfn(z)收敛半径R=1及φ(z)=∑∞n=1ann!zn,则可用函数:F(z)=∫∞0e-1Φ(tz)dt对f(z)进行解析延拓到区域G,G的边界为所有在f(z)的奇点与单位圆相切的直线。

Let f(z)=∑∞n=1anfn(z),R=1 be convergent radius and φ(z)=∑∞n=1ann!zn, then with function: F(z)=∫∞0e-1Φ(tz)dt f(z) can regmained in region G,the frontier of G be the unit circle's tangents that all of the point singularities can be on .