TEAM PROJECT. Laurent Series. (a) Uniqueness. Prove that

Chapter 16, Problem 16.1

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TEAM PROJECT. Laurent Series. (a) Uniqueness. Prove that the Laurent expansion of a given analytic function in a given annulus is unique. (b) Accumulation of singularities. Does tan (II:) have a Laurent series that converges in a region o < Izl < R? (Give a reason.) (c) Integrals. Expand the following functions in a Laurent series that converges for Izl > 0: I (et-I 2 L--- dr, ::: 0 1 I IZ sin t - --dt.

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