Complex Analysis: Double Keyhole Contour

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Today, we use contour integration to integrate 1/(x*sqrt(x^2-1)) from 1 to infinity.
  1. qncubed3
  2. complex analysis
  3. contour integration
  4. keyhole contour
  5. branch cut
  6. residue theorem
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Комментарии
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We can either just substitute x=sec(theta) and be done in a minute, or completely flex on others with this overkill^^

Rundas
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20:40 Do you have a name for this lemma? In case I would like to cite for refer to it in the future.

palmyjackson
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how arbitrary are the argument choices? can it cause contradictions?

ikarienator
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wtf is this 10:00 ? You do not show how it work.

nightmareintegral
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Thank you for this lovely demonstration!

XylyXylyX
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If you choose the new variable y = 1/x you get the integral of 1/√(1-y^2) from 0 to 1, which is arcsin[1]= π/2 .

renesperb
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Awesome!
And waiting for more spicy integrals....👍

carlosgiovanardi
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Hello Dear *QN3*
*I'M SO HAPPY YOU'RE HERE*
And also I'm so happy you finally decided to continue this playlist (complex analysis).
You know, you're on my top three; please be more active.
The long one ... I'm even more happier
Thank you

wuyqrbt
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im a bit late. finally the complex analysis is back

thepirateage
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At 6:00 why did you put arg(z) in arg(f). I thought z=0 is a pole?

quedinhminh
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This is funny, but beautiful, thank you

daigakunobaku
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In 10:25 how could you define those arguments and put the angle ?

minhquedinh