Laurent series expansion of complex functions
For each of the functions f(z) find the Laurent Series expansion on for the given isolated singularity (specify R). Then classify as an essential singularity, a pole (specify the order), or a removable singularity. Then find
See Attached
© BrainMass Inc. brainmass.com October 10, 2019, 6:56 am ad1c9bdddfhttps://brainmass.com/math/complex-analysis/laurent-series-expansion-complex-functions-561993
Attachments
Solution Preview
Hello and thank you for posting your question to BrainMass.
The solution is attached below in two files. The files are identical in content, only differ in format. The first is in MS Word format, while the other is in Adobe pdf format. Therefore you can choose the format that is most suitable to you.
suppose is an isolated singularity of f, then
is removable the Laurent expansion is a Taylor series - there are no negative powers of in the expansion.
is a pole of order n there are exactly n terms in the Laurent expansion with negative powers of
is an essential singularity there is infinite number of terms in the Laurent expansion with negative powers of
1.
(1.1)
There are two singularities for this ...
Solution Summary
The solution shows how to expand a complex function to a Laurent series, identify the type of singularity and find the residue.