An expression in functional analysis

  • Thread starter Charles49
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Are there any theorems concerning this expression
[tex]\frac{1}{z}f\left(\frac{1}{z}\right)[/tex]. I appreciate posts of any theorems you can think of.
 

Mute

Homework Helper
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The closest thing I can think of concerns [itex]f(1/z)/z^2[/itex]. If you have a complex function f(w) with a pole at infinity, then

[tex]\mbox{Res}_{w = \infty} f(w) = -\mbox{Res}_{z = 0} \frac{f(\frac{1}{z})}{z^2}[/tex]
 
87
0
The closest thing I can think of concerns [itex]f(1/z)/z^2[/itex]. If you have a complex function f(w) with a pole at infinity, then

[tex]\mbox{Res}_{w = \infty} f(w) = -\mbox{Res}_{z = 0} \frac{f(\frac{1}{z})}{z^2}[/tex]
Thanks, this was exactly what I was looking for!
 

Landau

Science Advisor
905
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Haha, sometimes a vague question can get the perfect answer immediately :)
 

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