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touqra
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How do you get the residue of this expression:
\frac{1}{(e^z - k)} where k is a constant.
\frac{1}{(e^z - k)} where k is a constant.
Finding the Residue of an Expression with a Constant
- Thread starter touqra
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- Constant Expression Residue
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SUMMARY
The discussion focuses on calculating the residue of the expression \( \frac{1}{(e^z - k)} \), where \( k \) is a constant. It emphasizes that if \( k = 0 \), the expression becomes \( \frac{1}{e^z} \), which is analytic. However, for \( k \neq 0 \), the expression introduces a singularity that is contingent upon the chosen contour for integration. Understanding the behavior of this expression is crucial for complex analysis applications.
PREREQUISITES- Complex analysis fundamentals
- Residue theorem application
- Contour integration techniques
- Understanding of singularities in complex functions
- Study the residue theorem in complex analysis
- Explore contour integration methods
- Investigate the behavior of \( e^z \) and its singularities
- Learn about different types of contours used in complex integration
Students and professionals in mathematics, particularly those specializing in complex analysis, as well as physicists and engineers dealing with integrals involving exponential functions.
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