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 April 6th, 2014, 06:34 PM #1 Senior Member   Joined: Jan 2014 Posts: 196 Thanks: 3 Verifying analytic part in example converges $\displaystyle f(z)= \frac{sin(z)}{z^4}=\frac{1}{z^3} - \frac{1}{3!z} + \frac{z}{5!}- \frac{z^3}{7!} + \frac{z^5}{9!}.....$ Would like to know how to verify that the analytic part... $\displaystyle \frac{z}{5!}- \frac{z^3}{7!} + \frac{z^5}{9!}.....$ converges. Thanks! April 7th, 2014, 03:53 PM #2 Global Moderator   Joined: May 2007 Posts: 6,834 Thanks: 733 The proof is a small variation on the proof that the series for sin(z) converges. Tags analytic, converges, part, verifying Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post ehh Trigonometry 7 June 20th, 2012 07:50 PM omo5031 Algebra 3 February 19th, 2012 07:45 PM cxc001 Calculus 3 September 9th, 2010 06:54 AM nedaiii Real Analysis 1 February 8th, 2009 07:15 PM tiffanyk12 Calculus 0 December 31st, 1969 04:00 PM

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