How to calculate the converge radius of a Laurent series

  • Thread starter kakarotyjn
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  • #1
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A method to get the Laurent series of a complex function is by undetermined coefficient.For example f(z)=cot(z)=cos(z)/sin(z).If we want to get the Laurent series of cot(z),we can expand cos(z) and sin(z) to Taylor series respect,then assume the series of cot(z) is [tex]a_{ - 1} z^{ - 1} + a_0 z^0 + a_1 z^1 + ...[/tex],

we can get a_-1,a_0... one by one.

But how to calculate its convergence radius?

Thank you!
 

Answers and Replies

  • #2
Gib Z
Homework Helper
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Just as regular power series are valid in the disc of largest radius that doesn't contain a singularity, Laurent series are valid in the largest annulus that doesn't contain any singularities.
 

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