- #1
oahsen
- 59
- 0
I have written this simple code fragment to the MATLAB for finding the residue(s) of the function 1/(z-i/9)^3;
b=[1];
a=[1 -i/3 -1/27 i/(729) ];
[r p k]=residue(b,a)
and get the following result;
r =
0
0
1
p =
0.0000 + 0.1111i
0.0000 + 0.1111i
0.0000 + 0.1111i
k =
[]
The poles are true. Function has a pole of order three at z=i/9 . However, there are two different values for the residue: 0 and 1. I could not get the meaning behind that? How can a function have different residue at the same point? Additionally if we assume MATLAB is right then the result of the contour integral should be 2pi*i at the unit circle. However, we can easily show that this contour integral is zero. So, is something wrong with the residue algorithm of MATLAB or there is something I do not consider?
b=[1];
a=[1 -i/3 -1/27 i/(729) ];
[r p k]=residue(b,a)
and get the following result;
r =
0
0
1
p =
0.0000 + 0.1111i
0.0000 + 0.1111i
0.0000 + 0.1111i
k =
[]
The poles are true. Function has a pole of order three at z=i/9 . However, there are two different values for the residue: 0 and 1. I could not get the meaning behind that? How can a function have different residue at the same point? Additionally if we assume MATLAB is right then the result of the contour integral should be 2pi*i at the unit circle. However, we can easily show that this contour integral is zero. So, is something wrong with the residue algorithm of MATLAB or there is something I do not consider?