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a) Prove that the series f(2) = Ee -" sin(nz) n=1 defines a holomorphic function in the strip -1 < Im(z) < 1.

a) Prove that the series f(2) = Ee -" sin(nz) n=1 defines a holomorphic function in the strip -1 < Im(z) < 1.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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a) Prove that the series f(2) = e" sin(nz) n=1 defines a holomorphic function in the strip -1< Im(2) < 1. b) Does f(z) have an analytic continuation outside the strip -1 < Im(z) < 1? In which maximal domain? Hint: Evaluate the series.
Transcribed Image Text:a) Prove that the series f(2) = e" sin(nz) n=1 defines a holomorphic function in the strip -1< Im(2) < 1. b) Does f(z) have an analytic continuation outside the strip -1 < Im(z) < 1? In which maximal domain? Hint: Evaluate the series.
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