Re: A question about essential singularity

In article <MfSOh.112058$fo5.93313@trnddc07>, TCL <tlim1@xxxxxxxxxxx>
wrote:

Suppose f(z) is a holomorphic function on the complex plane with 0
deleleted. Assume that f has an isolated essential singularity at 0.
Is it true that

int_C f(z) = a_{-1} 2pi i ?

where C is the unit circle and a_{-1} is the coefficient of z^{-1} in the
Laurent expansion of f.

(Of course, if 0 is a pole, this is true.)



Provided there are no other singularities inside the unit circle.

--
G. A. Edgar http://www.math.ohio-state.edu/~edgar/
.

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