I know that $$f:\mathbb C^*\to\mathbb C, \\ z\mapsto\frac{1}{2}\Big(z+\frac{1}{z}\Big)$$ is an analytic function since it is holomorphic. Is there any "basic" way to see that this function is analytic without knowing the equivalence of these two terms? Is there a general approach to such a problem?
2026-03-24 22:08:29.1774390109
Proving that a function is analytical without knowing $f$ holomorphic $\Leftrightarrow$ $f$ analytic
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