Note: Typo at 3:55 should be an element symbol instead of equality ... silly me

Without any doubt: You're *The King Of Complex analysis* on KZread. Please continue this playlist. Thank you 💖

@birdbeakbeardneck3617

4 ай бұрын

math505 is cool too

He sorta looks like Jacob Collier...

this channel is so f underrated ! .. the best on complex analysis thank you

@azzteke

2 жыл бұрын

underrated by whom please?

When I first did this integral and got the right answer, I knew finally that I really understood complex analysis.

@darcash1738

5 ай бұрын

I know nothing about it but I became interested in it rn when I saw him use it on an integral that I thought could only cleanly be done w/Feynman’s technique. Would you say if I were to fully learn all concepts used in this video(and ofc be able to replicate em in other problems), i would have learned the essence of complex analysis? Also, what would you describe the point of complex analysis now that you’ve become well-versed in it 😅 based on how it sounds, is it like a deep dive into the utility of the complex plane for solving problems?

*Happy first contour integral with chalk board* Yeah, I watched a whiteboard version of it before, but with some difficulty. But this one is great, in all aspects. And ... Please when you are busy, at least make short videos. Thank you so much dear *QN³* ❤️

Blackboard videos are noice.

Excellent!

wow this is great!

great job!

An interesting, alternative form for the final answer: I = (1/n) * Γ(1/n) * Γ(1-1/n) I = Γ(1+1/n) * Γ(1-1/n) I = B(1+1/n, 1-1/n)

Interesting the result looks like the reflection formula for the gamma function but with 1/n

you saved me thank you

A question: residue method can only be used to calculate definite or improper integrals but not for indefinite in order to obtain only the primitive?

That's pretty nice. Would it be possible to generalize this result for R=1?

Can you make a video explaining contour integrals?

Thanks for this great video and explanation. Just a question, at 7:16, should there be two or three poles in the lower right quadrant (positive Real, negative Imaginary)?

@qncubed3

2 жыл бұрын

It doesn't matter since this is only a rough sketch of where the poles could be. Depending on the value of n, the number and position of the poles will be entirely changed. The only pole that we are concerned about is the first one.

@ryanblais6208

2 жыл бұрын

@@qncubed3 ah ok, thank you!

@javiergilvidal1558

Жыл бұрын

@@qncubed3 It is not at all obvious, though nonetheless true, that the integral value remains the same if the pizza slice includes the first two nth-roots of (-1), or the first three, .... or in fact all of them, in which case you have the whole pizza minus a slice with no roots in its interior. Proving that the integral does not depend on how many residues you trap inside your region of integration would be a great exercise. I did it for the first two, and the result is far from obvious until the very end, when a magical simplification comes to save you in the nick of time! Will try to find the general answer tomorrow.

Greattttttt video! However, can n be non-integer?

all u need is the beta function then put into gamma form and use euler's reflection formula

Finalllllly ......

After a such long time....... :D

Thank you for that wonderful piece of delivery, pls, can you help when n=5 , I.e f(x) = 1/ x^5 + 1

Is there a way to compute the indefinite integral of this with complex analysis or do you have to have bounds?

@qncubed3

2 жыл бұрын

I'm not sure if contour integration can be used to evaluate indefinite integrals. However, here's a related post I found :) math.stackexchange.com/questions/1999869/evaluate-int-frac11xndx-for-n-in-mathbb-r

@Pommes736

2 жыл бұрын

@@qncubed3 I'm not interested in this school integral per se. I wanna know if it's possible in general for any function without any bounds.

@davidraveh5966

Жыл бұрын

@@Pommes736 If you want to gain intuition for things like this, use software to numerically solve your integrals for different bounds; this will inform you of the answer immediately, although to prove that they are equivalent may be difficult.

@Pommes736

Жыл бұрын

@@davidraveh5966 Oh you didn't understand my question. I can solve these integrals without problem, my question was if I can use THIS METHOD for INDEFINITE integrals.

A much simpler aproach, about how i solved it. Substitute x=t^1/n This makes dx=t^((1/n)-1)dt The given function resolves to the form of beta function. Which later simplifies into eulers reflection formula

There’s actually a better method divide the denominator and numerator with x^n and then apply partial fraction and then resolve the contour

Good

I would probably calculate it with Beta function then change it to Gamma function , finally i would finish it with reflection formula for Gamma

But why are you allowed to choose a contour that's only around a single pole? Why not choose a contour that encloses 2 poles? How diff would the answer be?

@qncubed3

2 ай бұрын

It is possible, but then you would have to calculate two residues

We are waiting ..... 🧐 It's me, looking at screen, for your notification 🧐

@qncubed3

2 жыл бұрын

Videos coming back by the end of this week :)

What if we replaced n by 5, how will the integfation be, and what will the answer be?? Do i just replace n by 5 in all the steps of the solution and in the final answer or what??

@harisserdarevic4913

6 ай бұрын

uh yeah thats what it means to solve something for a general variable n. it holds for any n>1 so you don't have to redo any work

@ayman1515

6 ай бұрын

​@@harisserdarevic4913 try it for n=5 using this method and try it using decompoaition and if you reached same answer then it is correct. I think for odd power, it has another way of solving

lovely accent as well!

@qncubed3

2 жыл бұрын

cheers, from straya mate

@ianmoog123

2 жыл бұрын

lovely country

@ianmoog123

2 жыл бұрын

I thought you were english or something by the way you dressed lol

I wish you were my classmate!

Bad boy you don't clean up your own mess 😤

this video looks like asian flammable maths

@qncubed3

2 ай бұрын

:O

Bêta fonction mène à la même résultat

Blackboard videos

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