Residue Calculus for Evaluating e^z/cosh z on Circle |z|=5

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SUMMARY

The discussion focuses on using residue calculus to evaluate the integral \(\oint_C \frac{e^z}{\cosh z} dz\) over the circle defined by \(|z|=5\). The user identifies the poles of the function, which occur at \(z = \frac{\pi i}{2} + \pi i k\) for integer values of \(k\). The user initially struggles with determining the number of poles within the specified circle but ultimately resolves the issue. This highlights the importance of understanding the locations of poles in complex analysis for evaluating integrals.

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  • Complex analysis fundamentals
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  • Familiarity with contour integration techniques
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Students and professionals in mathematics, particularly those studying complex analysis, as well as anyone looking to deepen their understanding of residue calculus and contour integration techniques.

David Laz
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I need to use residue calculus to evaluate:
[tex]\oint_C {\frac{{e^z }}{{\cosh z}}} dz[/tex]
where C is the circle |z|=5
My only problem (which is a stupid one) is working out how many poles the function has inside the circle. I know its going to have them at pi*i/2 + pi*i*k. This is probably a really stupid question, but I've left a lot of this course till the last minute. :(
 
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Worked it out. I'm an idiot for overlooking something so simple.
 

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