Answer to Question #252969 in Complex Analysis for Msa

Complex Analysis

Question #252969

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

Expert's answer

"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+..."

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