I know that Laurent series expands a function f(z) around a point even if it is not analytic at that point and the coefficients in the series expansion are given by
$$a_n =\frac{1}{2\pi i}\oint_C \frac{f(z)}{(z-c)^{n+1}}$$
The above formula is nothing but Cauchy's integral formula. But in my text book it says we can apply Cauchy's integral formula only if the function f(z) is analytic on and inside the curve C. But we already know Laurent series is true even when it is not analytic at that point.
What am I missing here?
Laurent series is not necessarily analytic everywhere but Cauchy's formula needs it to analytic everywhere. Seems contradictory!!