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cheeez
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There are a lot of definitions but what is the quickest way to see if a function is holomorphic? apply the cauchy riemann equations seems too slow. I thought if it doesn't have a z_bar in it, then it's automatically holomorphic. so for ex. polynomials are always holomorphic. on the other hand, 1/z on the unit circle is z_bar so it's not holomorphic but if you take the z_bar derivative of 1/z in the elementary calculus sense, it is 0. So as long as z can't be rewritten as z_bar it's fine to treat it as a constant? Are there things of this sort to watch out for?