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Unformatted text preview: f extends holomorphically to the entire domain Ω. a) First try a simple case when F is ﬁnite b) Try the case when F has ﬁnite number of accumulation points c) Try the general case. d) The problem still remains valid if F is a compact set of zero length (1dimensional Hausdorﬀ measure), try to extend your proof to this general case. Recall that F has zero length if it can be covered by a ﬁnite number of disks whose diameters sum up to a number as small as we wish. Problem 4 . Compute the following integral ∫ ∞ cos x (1 + x 2 ) 2 dx Hint. Consider the following complex function in the upper half plane f ( z ) = e iz (1 + z 2 ) 2...
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 Spring '11
 NA
 Logic, Taylor Series, Analytic function, Unit disk

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