Cauchy’s integral formula for derivatives indicates that if a function f is analytic at a point z0, then it possesses derivatives of all orders at that point. As a consequence, we will see that f can always be expanded in a power series at that point. On the other hand, if f fails to be analytic at z0, then we may still be able to expand it in a different kind of series known as a Laurent series. The notion of Laurent ...
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