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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6210 • Real Analysis

Fall 1995 • Question 9

Question

Math 6210 • Real Analysis Fall 1995 • Question 9

Find \[ \int _{\gamma _R}\frac {dz}{e^z-1} \] where \(\gamma _R\) is the curve \(|z|=R\) traversed counterclockwise and \(R\) is a positive number such that \(\gamma _R\) does not pass through a zero of \(e^z-1\).

Raw LaTeX

Find
\[
\int_{\gamma_R}\frac{dz}{e^z-1}
\]
where \(\gamma_R\) is the curve \(|z|=R\) traversed counterclockwise and \(R\) is a
positive number such that \(\gamma_R\) does not pass through a zero of \(e^z-1\).

Topic Tags

Lebesgue Integration Zeros of Holomorphic Functions and the Identity Theorem