(1-e^(-z))/z^4z=0是几阶极点题目是f（z)=(1-e^(-z))/z^4,问z=0是几阶极点

Question

(1-e^(-z))/z^4 z=0是几阶极点
题目是f（z)=(1-e^(-z))/z^4,问z=0是几阶极点

Answer 1

[级数展开e^z=1+z+z^2/2+z^3/3 可见z是2阶极点] lim(z→0)(z-0)*[sinz/z^2] =lim(z→0)sinz/z =1 [级数展开sinz=z-z^3/3