How and when to use Cauchy's integral formula

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    Formula Integral
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Homework Help Overview

The discussion revolves around the application of Cauchy's integral formula in complex analysis. The original poster seeks clarification on when and why to use this formula, expressing confusion regarding their specific problem and the values they have assigned to the variables involved.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the conditions under which Cauchy's integral formula is applicable, with some questioning the correctness of the original poster's values for the function and points involved. There are attempts to clarify the relationship between the integral and the function being evaluated.

Discussion Status

The discussion includes various interpretations of the problem, with some participants providing guidance on the use of the formula and the importance of properly defining the function. However, there is no explicit consensus on the original poster's specific situation, and the conversation has shifted towards the need for clearer presentation of the work involved.

Contextual Notes

There are mentions of guidelines regarding the submission of handwritten work, indicating a preference for typed content to facilitate assistance. This suggests a constraint on how participants can present their attempts for review.

MissP.25_5
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Hello.
How do I know when to use Cauchy integral formula. Why do we use the formula in this question? As you can see in my attempt, I got stuck.
Are my values for f(z), z, z​0 here correct?
 

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You got the right answer, since f(zo)=1.
You use the Cauchy integral when you have to evaluate an integral that matches the pattern of a Cauchy integral!
Sometimes, the contour needs to be closed to get a match and the integral on the closing path can be evaluated by some other means.
The Cauchy integral is very useful in physics and in signal theory.
 
maajdl said:
You got the right answer, since f(zo)=1.
You use the Cauchy integral when you have to evaluate an integral that matches the pattern of a Cauchy integral!
Sometimes, the contour needs to be closed to get a match and the integral on the closing path can be evaluated by some other means.
The Cauchy integral is very useful in physics and in signal theory.

No, I just solved it and f(z) is not 1, but 1/(z-1).
 
You proved that your integral is 2 Pi I * the Cauchy integral of f(z)=1 around z=I .
Therefore, your integral is 2 Pi I f(I) = 2 Pi I .
 
MissP.25_5 said:
Hello.
How do I know when to use Cauchy integral formula. Why do we use the formula in this question? As you can see in my attempt, I got stuck.
Are my values for f(z), z, z​0 here correct?

I never look at photo attachments of handwritten work; in fact, if you read the "PF Guidelines" post by vela, you will see that you are not supposed to use them except for very special circumstances---for several good reasons. You should take the trouble to type out your work if you want the helpers to take the trouble to offer free assistance.
 
Ray Vickson said:
I never look at photo attachments of handwritten work; in fact, if you read the "PF Guidelines" post by vela, you will see that you are not supposed to use them except for very special circumstances---for several good reasons. You should take the trouble to type out your work if you want the helpers to take the trouble to offer free assistance.

Exactly! Thread locked. Please create a thread where you write out your work.
 

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