Cauchy's Integral Formula problem

  • Thread starter paddo
  • Start date
  • #1
11
0
How would you integrate sin(z)/(z-1)^2 using Cauchy's Integral Formula? 1 is in C.

Cheers
 

Answers and Replies

  • #2
2,112
18
Integration domain would be relevant.
 
  • #3
11
0
All it says is that "C is any simple closed contour around both z = 1 and z = i"
 
  • #4
2,112
18
The knowledge that the contour goes once around z=1 should be enough. The comment on point z=i looks like misdirection.

I believe that actually you already know what you want there, assuming that you know the Cauchy's integral formula. It's just that the 1/(z-1)^2 is confusing?
 
  • #5
11
0
Yeah. I know the formula.

I did 1/(z-1)^2 but didn't come out as partial fractions.
 
  • #6
2,112
18
There exists coefficients [itex]a_{-2}, a_{-1}, a_0, a_1, \ldots[/itex] so that

[tex]
\frac{\sin z}{(z-1)^2} = \frac{a_{-2}}{(z-1)^2} \;+\; \frac{a_{-1}}{z-1} \;+\; a_0 \;+\; a_1(z-1) \;+\; \cdots
[/tex]

For integration, you need to know the [itex]a_{-1}[/itex].
 

Related Threads on Cauchy's Integral Formula problem

  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
7
Views
1K
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
2
Views
12K
  • Last Post
Replies
8
Views
3K
  • Last Post
Replies
2
Views
890
Replies
1
Views
1K
Replies
2
Views
3K
  • Last Post
Replies
1
Views
2K
Replies
2
Views
741
Top