Define a holomorphic function $f\colon\mathbb{C}\setminus[-1,1] \longrightarrow \mathbb{C}$ such that $\forall z \in \mathbb{C}\setminus[-1,1] \ \left( (f(z))^{2} = z^{2} - 1\right)$ and $f(2)=\sqrt{3}$.
Define square root function over the complex numbers.
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complex-analysis
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1just try square root of what is given to you, i.e. $e^{\frac{1}{2}\log(z^2-1)}$ – 2012-11-14
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0"The"? There are two square roots. Not only that, where sould the logarithm be defined? – 2012-11-14