Unformatted text preview: (2) Compute Z ∞ x 2 x 4 + x 2 + 1 dx. (3) Compute Z ∞∞ cos πx x 22 x + 2 dx by integrating f ( z ) = e πiz z 22 z +2 over a semicircular path. (4) (Quals ’06) Let f be a holomorphic function on  z  < 1. Assume f ( 1 n ) ∈ R for n ≥ 2. Prove f ( x ) ∈ R for all1 < x < 1. (Hint: Use Problem 4 from HW 8.) 1...
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This note was uploaded on 02/05/2012 for the course MATH 703 taught by Professor Schep during the Fall '11 term at South Carolina.
 Fall '11
 Schep

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