Trying to get a Laurent expansion of a symbolic function – mathematica.stackexchange.com

Im trying to find the Laurent expansion of the function $$f(z):=\frac{a-b}{(z-a)(z-b)},\quad\text{for }0<|a|<|b|$$ around $z=0$ in the annulus defined by $A:=\{z\in\Bbb C:|a|<|z|<|b|\}$. ...

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