Why Does lnZ Not Represent an Isolated Singularity?

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The discussion centers on why ln(z) is not considered an isolated singularity, primarily due to its inability to be defined as holomorphic in the disk after removing zero, as it has multiple branches. Participants also address a homework problem involving the integration of [(log x)^4]/[1+x^2] from 0 to infinity, emphasizing the importance of understanding branch cuts in relation to the integrand. There is a suggestion to avoid posting new questions in existing threads and to start a new thread instead. The poles of the function are identified as x = ±i. Understanding these concepts is crucial for tackling the integration problem effectively.
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why lnZ is not isolated singularity?
 
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Because you can't define ln(z) to be holomorphic in the disk after removing 0. It has multiple branches.
 
Questions on Poles

I am trying to do my homework on:

Integration form 0 to infinity of [( log x)^4 ]/[1+x^2] dx =

by first defining what is a branch cut and how it will fit into the above integrand.

Thanks

Marie
 


logmarie said:
I am trying to do my homework on:

Integration form 0 to infinity of [( log x)^4 ]/[1+x^2] dx =

by first defining what is a branch cut and how it will fit into the above integrand.

Thanks

Marie

I don't recommend posting a brand new question onto an existing thread. Start a new one. While you're doing that figure out how to start the problem so you can post an attempt. Where are the poles?
 
How do I start the new threads?

Thanks
 
The poles is x= +/- i
 
logmarie said:
How do I start the new threads?

Thanks

Go to the Calculus and Beyond forum and under Forum Tools you'll find start new thread.
 

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