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Exercise:
Find the Laurent-series for fzfracz+frac-z+frac-z for the rings abcliste abc |z| abc |z-| abc |z-| abcliste

Solution:
abcliste abc On |z| we have that fracz fracz frac-z _ngeq z^n frac-z fracfrac-fracz frac_ngeq leftfracright^n which gives in total Rightarrow fz fracz+_ngeq z^n+frac_ngeq leftfracright^n abc On |z-| we have that fracz frac--z _ngeq -z^n frac-z frac-z frac-z frac-z- _ngeq -^nleft-zright^n which gives in total Rightarrow fz _ngeq -z^n+frac-z abc On |z-| we have that fracz frac--z frac_ngeq leftfrac-zright^n frac-z frac-z- fracfrac-z-frac-z frac-z_ngeq left frac-zright^n frac-z frac-z which gives in total Rightarrow fz frac-z+frac-z_ngeq left frac-zright^n+frac_ngeq leftfrac-zright^n abcliste
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Exercise:
Find the Laurent-series for fzfracz+frac-z+frac-z for the rings abcliste abc |z| abc |z-| abc |z-| abcliste

Solution:
abcliste abc On |z| we have that fracz fracz frac-z _ngeq z^n frac-z fracfrac-fracz frac_ngeq leftfracright^n which gives in total Rightarrow fz fracz+_ngeq z^n+frac_ngeq leftfracright^n abc On |z-| we have that fracz frac--z _ngeq -z^n frac-z frac-z frac-z frac-z- _ngeq -^nleft-zright^n which gives in total Rightarrow fz _ngeq -z^n+frac-z abc On |z-| we have that fracz frac--z frac_ngeq leftfrac-zright^n frac-z frac-z- fracfrac-z-frac-z frac-z_ngeq left frac-zright^n frac-z frac-z which gives in total Rightarrow fz frac-z+frac-z_ngeq left frac-zright^n+frac_ngeq leftfrac-zright^n abcliste
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ca, eth, laurent, series
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Difficulty
(3, default)
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0 (default)
Language
ENG (English)
Type
Descriptive / Quality
Creator rk
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