Taylor Series Expansion About the Point i

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SUMMARY

The discussion focuses on calculating the radius of convergence for the Taylor series of the function \( \frac{1}{z^2-2z+2} \) about the point \( i \). Participants emphasize the importance of identifying the poles of the function to determine the radius of convergence. The poles for this function are located at \( z = 1 \pm i \), which directly influences the radius of convergence. Understanding these poles is crucial for accurately expanding the series.

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Taylor Series Expansion About the Point "i"

Homework Statement



Calculate the radius of convergence of the Taylor series for

\frac{1}{z^2-2z+2}

about the point i.

The Attempt at a Solution



I can find the radius of convergence if I can determine the expansion but I can't seem to spot the pattern...

Any help will be appreciated (please see attached).
 

Attachments

Physics news on Phys.org


how about consdering where the poles of the function are...
 


We haven't actually covered that yet, but I'll have a look thanks!
 

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