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Unformatted text preview: J (c) := I C (c) cosh z d z (2 ln 2-z ) 5 . 3. (Problems 14.4.5 and 7, p. 681) Identify all singular points of the functions f (a) ( z ) := z-1 z 3 ( z-2) and f (b) ( z ) := 2-z 1-z 2 . Develop a Laurent series expansion about the origin for each in each annular ring bounded by those singular points. Use the interior expansion to calculate each residue at the origin. 4. (Problem 14.4.10, p. 682) For each of the following functions, say whether the indicated point is regular, and essential singularity, or a pole. If it is a pole, say what order it is. a. e z-1 z 2 + 4 at z = 2i b. tan 2 z at z = 2 c. 1-cos z z 4 at z = 0 d. cos z- at z =...
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- Fall '10