a) Prove that the series f(2) = e" sin(nz) n=1 defines a holomorphic function in the strip -1

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Extracted 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="">