Unformatted text preview: f ( z ), ±nd the order of the zero at z = 0. ( a ) cos( z 2 ) − 1 ( b ) sin( z 3 ) ( c ) ( e z − 1) 3 ( d ) z 7 − 12 z 5 + z 3 5. a) Suppose that f ( z ) is an entire function, with a pole at z = ∞ of order m ∞ ≥ 1. Show that f ( z ) is a polynomial of degree m ∞ . b) Suppose that f ( z ) is analytic at all points of C −{ z } , and f ( z ) has a pole of order m at z = z and a pole of order m ∞ at z = ∞ . Show that f ( z ) = P ( z ) Q ( z ) where P ( z ) and Q ( z ) are polynomials of ±nite degree. 1...
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 Fall '11
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 Math

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