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nugget
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Homework Statement
For f(z) = 1/(1+z^2)
a) find the taylor series centred at the origin and the radius of convergence.
b)find the laurent series for the annulus centred at the origin with inner radius given by the r.o.c. from part a), and an arbitrarily large outer radius.
Homework Equations
for a) (sum from j = 0 to infinity)
f(z) = [itex]\Sigma[/itex] [(f[itex]^{j}[/itex](0))[itex]\div[/itex](j!)] [itex]\times[/itex] z[itex]^{j}[/itex]
for b) laurent series formula?
The Attempt at a Solution
From what I understand, the radius of convergence is from Zo (in this case, the origin) to the closest point where f(z) isn't analytic. f(z) isn't analytic at i or -i. This function is a circle, discontinuous at i and -i. So, by inspection(?), the r.o.c. should be 1.
I don't get how to input the information I have into the formula for a). I think that in understanding this, finding the laurent series should be simplified.
Thanks