We know that the set $A=\Bbb C-S$ where $S$=$\{z:z=yi, |y|\geq b>0\}$ with real numbers $y$ and $b$ is a region. I would like to determine a branch of logarithm $f(z)$ in the region $G$=$\{z:z\in$A$, Im(z)>0\}$ such that $f(\frac{a}{2}i)=ln(\frac{a}{2})-\frac{3}{2}i\pi\,$ and how many functions having such properties exist. Thank you very much in advance.
Determining a branch of logarithm and the number of it
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complex-analysis
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0Choose the branch cut as the ray from $ib$ to $i\infty$. And choose the sheet with $-3\pi/2\le \arg(z)<\pi/2$. – 2017-01-21
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0Thank you very much for your reply. Could you kindly explain a little more in detail as I am struggling to grasp the concept. – 2017-01-21