The principal part of the Laurent series of f (z) = (1-e^{2z})/z^4 around zero is -2/z^3 - 4/z^2 - 8/z -2/z^3 - 2/z^2 - 4/3z 2/z^3 + 2/z^2 + 4/3z 0 -1/z^3 - 1/2z^2 - 1/6z
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Recall that the exponential function has a power series representation: e^x = 1 + x + x^2/2! + x^3/3! + ... for all x. So, e^(2z) = 1 + 2z + (2z)^2/2! + (2z)^3/3! + ... Now, we can find the Laurent series of f(z) by subtracting e^(2z) from L: Show more…
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