Purchase Solution

Laurent series expansion of complex functions

Not what you're looking for?

Ask Custom Question

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

Purchase this Solution

Solution Summary

The solution shows how to expand a complex function to a Laurent series, identify the type of singularity and find the residue.

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

There are two singularities for this ...

Purchase this Solution

Free BrainMass Quizzes
Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.

Solving quadratic inequalities

This quiz test you on how well you are familiar with solving quadratic inequalities.

Probability Quiz

Some questions on probability

Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.