Get the Laurent series expansion or f(z) =
in the intervals;
(i) |z-1|<1 and
(ii) 1<|z-1|< 2
Now I don't have much trouble finding the Laurent series expansions but am not sure how to do it for specific intervals.
For example in (ii) of this problem i would get the Laurent expansions for
for interval 1<|z-1|<2
and then get the expansions for
for 1<|z-1|<2,and add them all together. The textbook(correctly, just not sure why yet) just uses the expansion of
for |z-1|<2 and adds to it the expansion of
for 1<|z-1|. I'm not sure as to the procedure or the thinking behind getting Laurent expansions for these types of intervals
r1<|z-zo|< r2. Any help is much appreciated.