Register to reply

Expanding in powers of 1/z (Laurent series)

by Harudoz
Tags: 1 or z, expanding, laurent, powers, series
Share this thread:
Feb20-12, 12:38 PM
P: 2
The text book used in one of my courses talks about expanding functions in powers of 1/z aka negative powers of z.

The problem is that I cannot recall that any previous course taught me/challenged me on how to expand functions in negative powers. For example, Taylor series only have positive powers.

Is there a general method of expanding in negative powers, like for Taylor series, or are there at best similar methods for similar functions?

I fear I have overlooked something elementary here, because I feel strangely clueless about this one (and Internet searches have made me no wiser). The textbook only gives examples of the results of expansion in 1/z, but never gives any details on how it is done.
Phys.Org News Partner Science news on
Fungus deadly to AIDS patients found to grow on trees
Canola genome sequence reveals evolutionary 'love triangle'
Scientists uncover clues to role of magnetism in iron-based superconductors
Feb20-12, 01:11 PM
Sci Advisor
PF Gold
P: 4,500
Is this a complex analysis course, or is it something that had complex analysis as a prerequisite?

Practically, to calculate these you can often do standard Taylor series calculations
[tex]f(x)=\frac{x}{1-x} = \frac{1}{1-1/x}[/tex]

we know how to expand 1/(1-1/x) using the Taylor series for 1/(1-x)
[tex] f(x) = 1+\frac{1}{x}+\frac{1}{x^2}+\frac{1}{x^3}+...[/tex]
and this is valid as long as |x|>1
Feb20-12, 02:44 PM
P: 2
It's a physics course without physics, if that makes any sense. To answer the question though, complex analysis is a part of the course rather then a prerequisite (e.g. it includes the most basic proofs/definitions for differention of functions of a complex variable).

I do recall seeing the Taylor expansion you introduced (in an introductory course in astropysics, as a matter of fact).

Anyway, I guess my question has been answered.

Register to reply

Related Discussions
Expanding functions in increasing powers Calculus 1
Geometric series. Find the sum of the series. Powers. Precalculus Mathematics Homework 2
Laurent series: addition and multiplication of series Calculus & Beyond Homework 1
Even function has a Laurent decomposition of even functions and even powers of z Calculus 3
Laurent series Calculus & Beyond Homework 8