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dm4b
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- TL;DR Summary
- From Proof of Residue Theorem in Mary Boas' Text
Hello,
I am currently reading about the Residue Theorem in complex analysis. As a part of the proof, Mary Boas' text states how the a_n series of the Laurent Series is zero by Cauchy's Theorem, since this part of the Series is analytic. This appears to then be related to convergence of the a_n series.
I suppose convergence and analyticity seem to go together on an intuitive level, but I am having a hard time with the details of why this is so, especially as to how it would relate back to the Cauchy-Riemann conditions for analyticity.
Can anyone offer further insights here for me?
Thanks!
dm4b
I am currently reading about the Residue Theorem in complex analysis. As a part of the proof, Mary Boas' text states how the a_n series of the Laurent Series is zero by Cauchy's Theorem, since this part of the Series is analytic. This appears to then be related to convergence of the a_n series.
I suppose convergence and analyticity seem to go together on an intuitive level, but I am having a hard time with the details of why this is so, especially as to how it would relate back to the Cauchy-Riemann conditions for analyticity.
Can anyone offer further insights here for me?
Thanks!
dm4b