Answer to Question #252969 in Complex Analysis for Msa

Question

Find the laurent series for (1-exp2z)/z

Answer 1

$f(z)=\displaystyle{\sum_{n=0}^{\infin}}c_n(z-z_0)^n$

$c_n=\frac{f^{(n)}(z_0)}{n!}$

$z_0=0$

$1-e^{2z}=-2z+2z^2-4z^3/3+2z^4/3-4z^5/15+...$

$\frac{1-e^{2z}}{z}=\frac{1}{z}(1-e^{2z})=-2+2z-4z^2/3+2z^3/3-4z^4/15+...$