I'm trying to understand how to find a Laurent series for a function.
The Laurent series is given by $$f(z) = \sum^\infty_{n =-\infty} \frac{1}{2\pi i} \oint_C \frac{f(\epsilon)}{(\epsilon -a)^{n+1}}d\epsilon (z-a)^n$$
However, every example I found seems not to use this formula.
For $$f(z) = \frac{sinz}{z^2}$$ at the origin
How it works? Should I just plug a = 0 then integrate f(z). I'm really not sure how it works.