Tan z 1 z z3 6 sin z a0 a1 z a2 z 2 a3

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Unformatted text preview: power series is valid on a disc of radius 1 (= distance between 0 and 1, which is the nearest point where the function is not analytic) 16. tan z = 1 z − z3 + . . . = 6 sin z = a0 + a1 z + a2 z 2 + a3 z 3 + . . . ⇒ cos z 1 1 − z2 + . . . 2 a0 a1 = a0 + a1 z + − + a2 z 2 + − + a3 z 3 + . . . ⇒ 2 2 ⎧ ⎧ ⎪a0 = 0 ⎪0 = a0 ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨a = 1 ⎨1 = a 1 1 ⇐⇒ . a0 ⎪ ⎪− 2 + a2 = 0 ⎪a2 = 0 ⎪ ⎪ ⎪ ⎪ ⎪ a1 ⎩a = 1 ⎩− + a = − 1 3 3 2 6 3 a0 + a1 z + a2 z 2 + a3 z 3 + . . . The power series is valid...
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This note was uploaded on 12/05/2013 for the course MATH 334 taught by Professor Thind during the Summer '13 term at University of Toronto- Toronto.

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