I have written this simple code fragment to the matlab for finding the residue(s) of the function 1/(z-i/9)^3;(adsbygoogle = window.adsbygoogle || []).push({});

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?

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# A problem about residues(is matlab wrong?)

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