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March 26th, 2014, 03:08 AM | #1 |
Newbie Joined: Mar 2014 Posts: 5 Thanks: 2 | Detirmine where a laurent series is analytic
I have the following series and have to discuss where it is analytic g(z)= sum_{n=1}^infinity ( i( n^2+3)/(3*(2n^2-1)))^n * (z^n + z^-n) This is a laurent series. I found that without the negative powers of z, the series has a radius of converge of 1/6. g(z) is abviously not analytic at z=0. But I thought the idea was to find some anulus where the whole thing is analytic. How can I do this with z^-n part? or is the answer as easy as we need |z|<1/6 and z not equal to zero, and in this case, how can I show this? Thanks chanman |
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March 26th, 2014, 08:03 AM | #2 |
Math Team Joined: Sep 2007 Posts: 2,409 Thanks: 6 | Re: Detirmine where a laurent series is analytic
Since the |
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March 26th, 2014, 12:51 PM | #3 |
Newbie Joined: Mar 2014 Posts: 5 Thanks: 2 | Re: Detirmine where a laurent series is analytic
That is wrong to say because if the laurent series does not converge, then the function g(z) is not analytic
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analytic, detirmine, laurent, series |
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