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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: 6,732 Thanks: 689 
The proof is a small variation on the proof that the series for sin(z) converges.


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analytic, converges, part, verifying 
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