Areas in developing laurent series

Click For Summary

Homework Help Overview

The discussion revolves around developing a Laurent series for the function f(x) = \frac{-2}{z-1} + \frac{3}{z+2}. Participants are examining the appropriate annular regions for convergence, particularly focusing on the distances from singularities and the implications of these distances on the series development.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants are exploring the correct annular region for the Laurent series, questioning the validity of the intervals provided for convergence. There is a discussion about the relationship between the regions 0<|z-1|<3 and 0<|z-1|<1, and whether the latter is contained within the former.

Discussion Status

The conversation is ongoing, with some participants providing insights into the relationship between the regions of convergence. There is acknowledgment of the confusion regarding the specified intervals, but no consensus has been reached on the implications of these regions for the series development.

Contextual Notes

Participants are working under the constraints of developing the series around specific points and are addressing the implications of singularities and convergence intervals. There is mention of separate intervals and the need to clarify the conditions under which the series converges.

nhrock3
Messages
403
Reaction score
0
[tex]f(x)=\frac{-2}{z-1}[/tex]+[tex]\frac{3}{z+2}[/tex]
our distance is from -2 till 1
we develop around 1
so our distances are 3 and zeo
so our areas are
0<|z-1|<3
0<|z-1|
3>|z-1|
but i was told to develop around

0<|z-1|<1
there is no such area
?
 
Physics news on Phys.org
0< |z- 1|< 1 is -1< z< 1 and also [itex]z\ne 0[/itex]- two separate intervals.
 
nhrock3 said:
[tex]f(x)=\frac{-2}{z-1}[/tex]+[tex]\frac{3}{z+2}[/tex]
our distance is from -2 till 1
we develop around 1
so our distances are 3 and zeo
so our areas are
0<|z-1|<3
0<|z-1|
3>|z-1|
but i was told to develop around

0<|z-1|<1
there is no such area
?
The region 0<|z-1|<1 lies completely within 0<|z-1|<3, right? So if you find the Laurent series that converges in 0<|z-1|<3, it will obviously converge when 0<|z-1|<1.
 
thanks
:)
 

Similar threads

  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 7 ·
Replies
7
Views
2K
  • · Replies 9 ·
Replies
9
Views
2K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 7 ·
Replies
7
Views
2K
  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 12 ·
Replies
12
Views
6K
Replies
8
Views
2K
  • · Replies 2 ·
Replies
2
Views
4K