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Where is the function $(\cos (z))^{1\over 2}$ analytic? In other words, where in the complex plane $\mathbb C$ is the above function's series representation convergent?

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    It depends on what you mean by $(\phantom z)^{1/2}$.2012-02-19
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    @DylanMoreland: What do you mean? Suppose I take the principal branch?2012-02-19

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