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**sashikanth** Hi. Can you help me with deriving the Laurent series for $\displaystyle f(z) = e^{1/z} $ . I can derive it by substituting $\displaystyle 1/z $ for $\displaystyle z $ in the taylor series expression for $\displaystyle f(z) = e^z $ but I was trying to derive the Laurent Series using the integral formulae for the coefficients. When I do that, the integrals of the coefficients of the positive powers of z fail to vanish.

I would appreciate it a lot if someone took the trouble of pointing out how they vanish. Thank you!