求函数在奇点处的留数;1+z^4/(z^2+1)^3
问题描述:
求函数在奇点处的留数;1+z^4/(z^2+1)^3
答
f(z) = (1 + z⁴)/(z² + 1)³z = ± i 都是f(z)的3阶奇点Res[f(z),i] = 1/(3 - 1)! · lim(z→i) d²/dz² [(z - i)³ · (1 + z⁴)/(z² + 1)³]= (1/2) · lim(z→i) [- 1...