Solve Urgent Problem: 2 - Very Important for My Lesson

Thread starter isolet
Start date Dec 7, 2011
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SUMMARY

The discussion centers on the mathematical concept of residues in complex analysis, specifically addressing the identification of poles and their orders in integrands. The user clarifies that "C_R" is not a zero but part of the contour, emphasizing the importance of distinguishing between zeros of the denominator and poles of the integrand. A general formula for calculating residues at poles is referenced, indicating its relevance for solving complex integrals.

PREREQUISITES

Understanding of complex analysis concepts, particularly poles and residues.
Familiarity with contour integration techniques.
Knowledge of integrands and their behavior near singularities.
Ability to apply general formulas for residues in practical scenarios.

NEXT STEPS

Study the general formula for calculating residues at poles in complex analysis.
Learn about contour integration and its applications in evaluating complex integrals.
Explore the relationship between zeros of the denominator and poles of integrands.
Practice solving integrals involving poles of various orders using residue theory.

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Students and professionals in mathematics, particularly those studying complex analysis, as well as educators preparing lessons on residues and contour integration.

Dec 7, 2011

isolet

Sorry for other problem but very important for my lesson.

http://a1112.hizliresim.com/s/7/yv46.jpg

Last edited by a moderator: May 5, 2017

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Dec 7, 2011

HallsofIvy

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No, "[itex]C_R[/itex]" is not a "a zero", it is part of your contour. Perhaps you meant that i is a zero of the denominator and so is a pole, of order p, of the integrand. There is a general formula for the residue at a pole.