My Math Forum  

Go Back   My Math Forum > College Math Forum > Complex Analysis

Complex Analysis Complex Analysis Math Forum


Reply
 
LinkBack Thread Tools Display Modes
March 15th, 2012, 04:03 AM   #1
Newbie
 
Joined: Jan 2011

Posts: 20
Thanks: 0

Mistake with a simple residue problem!

(First I will forget the that is required when calculating every residue as it is not important here)

Calculate the residue at the simple pole for the function

If I use "The Residue at a Pole" lemma which states: Let be a pole of order of so that , for some g, analytic at with , then

For my function, I have simple poles (which is why I post a simpler an non-general version of the lemma), but when I apply this Lemma to find residue at my pole, I have:


This gives me:

But this is incorrect!

The correct answer is

Where is this 1/2 coming from??

And similarly, I face another problem:

Find the residue at the point for the function

At -1/3 I have a pole of order 2, so I rewrite , differentiate (because I do not have a simple pole, it is of order 2 => differentiate once) and insert in , which gives me
But this is also incorrect, as the correct value is , which is ...

Where are these 1/2 and 1/9 terms coming in??
omega is offline  
 
March 15th, 2012, 08:19 AM   #2
Math Team
 
Joined: Nov 2010
From: Greece, Thessaloniki

Posts: 1,990
Thanks: 133

Math Focus: pre pre pre pre pre pre pre pre pre pre pre pre calculus
Re: Mistake with a simple residue problem!

[color=#000000]Ok you confused me! You have ,





for the other one you have a second order pole at z=-3. Use the formula , in our case n=2 and





for the pole at write f in the following form and follow the above steps
.[/color]
ZardoZ is offline  
Reply

  My Math Forum > College Math Forum > Complex Analysis

Tags
mistake, problem, residue, simple



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Modulo Residue problem unm Number Theory 4 December 1st, 2012 05:42 PM
Can someone fix my mistake livestrong136 Calculus 1 May 8th, 2012 05:02 AM
Is there any mistake bobar77 Algebra 8 February 17th, 2012 10:37 PM
Interesting Problem With mistake in solution shurik Real Analysis 3 January 16th, 2011 10:07 AM
where is the mistake?? islam Calculus 6 December 3rd, 2010 08:33 PM





Copyright © 2019 My Math Forum. All rights reserved.