Contour Integral leads to Euler's Reflection Formula

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Complex Analysis: Contour Integral x^(a-1)/(1+x) from 0 to infinity
  1. Math Solving Channel
  2. Euler's reflection formula
  3. Contour Integral
  4. Complex analysis
  5. Complex integral
  6. gamma(x) gamma(1-x)
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Комментарии
Автор

Great.
I love complex analysis and ... Of course, I love this video too.
Thank you so much.

wuyqrbt
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Really good description of the solution. Thanks!

jbergamp
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great video! this integral is very useful!

witness
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Why not plug in e^(2*pi*i)=1 at time=2.34 without carrying it further?

צביקלברמן
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Hi
Just like in C3 we took ze^(2pi*i), why dont we do the same (i.e. z -> ze^(pi*i) = -z)when calculating similar integral of sinx/x (in case of tunnel contour)

psp.a
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Why don't the integrals along paths C1 and C3 sum to 0? Intuitively, it seems that they should, although I understand your explanation.

eamon_concannon
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Noice!! Another way is sub z=e^x so you get integral e^(ax)/(1+e^x) from -inf to inf and solve with contour integration over the rectangle -inf to inf (real axis) and 0 to 2pi(Im axis).😀

yoav
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Looks very advanced math.
Why keyhole is needed here? Test case?
What is the result if its not complex analysis case?

jarikosonen
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can you do this for the same integrand but integrated from 0 to 1 instead?

xulq
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I think you should relefect how many videos you upload

praxeria