Get solution: Expand the given function in a Laurent series that converges for 0 < I:: -
Chapter 16, Problem 16.1.8(choose chapter or problem)
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 (1/z) have a Laurent series that converges in a region 0 < |z| < R? (Give a reason.)
(c) Integrals. Expand the following functions in a Laurent series that converges for |z| > 0:
\(\frac{1}{z^{2}} \int_{0}^{z} \frac{e^{t}-1}{t} d t, \quad \frac{1}{z^{3}} \int_{0}^{z} \frac{\sin t}{t} d t\).
Text Transcription:
1 / z^2 int_{0}^{z} e^t - 1 / t dt, 1 / z^3 int_0^z sin t / t dt
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