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Calculating one BRUTAL Integral! Deriving Euler's Reflection Formula the RIDICULOUS way!

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Today we are going to go overbored! We are going to prove Euler's reflection formula today using the integral definition of the gamma function! What'S going to pop out is basically just a special case of the so-called Beta function. Surprisingly enough, we also get a single integral out of this whole ordeal, which is going o evaluate to teh pole expansion of the cosecans! =) Enjoy :)
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Опубликовано:

22 авг 2024

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Комментарии : 97

@HansFlamme 5 лет назад

After this brutal Integral, france will surrender

@HansFlamme 5 лет назад

@@PapaFlammy69 ❤️

@robinpetersson5290 5 лет назад

You misspelled. It's called Wheeler's Reflection Formula ;) Love your vids

@x15cyberrush9 5 лет назад

man those Chinese things got me you're a real meme lord😂😂😂😂😂😂😂

@gergodenes6360 5 лет назад

6:55 "So how can we express t?" - easy just plug the s you have just calculated into Omega * s \*proceeds to not do that* But... it was trivial all along :'C

@megauser8512 4 года назад

I know right!

@gdsfish3214 5 лет назад

"Friends is a great documentary set in the city of hongkong" - Blazinskrubs aka Podel I almost shed a tear when I heard the audio, I see you're a man of culture as well.

@federicovolpe3389 5 лет назад

When you're studying for HSK1 and take a quick break, you open Flammy's vid and it starts with him speaking chinese 0_o

@gregoriousmaths266 4 года назад

Lmaoooooo that intro I love the Chinese part of ur vids Please bring it back

@PapaFlammy69 4 года назад

@josephholten5088 5 лет назад

great video flammy! i love these kind of videos. because o this kind of content i've loved your channel

@math3ma70 4 года назад

I have tried the same brutual integration and ended up getting a infinite series but not the actual formula..... So the best approach to prove this identity is by using the contour integration of x^z-1/1+x BTW really loved your video....

@willnewman9783 5 лет назад

Good video. I am glad you are sticking with math content on your channel

@redvel5042 5 лет назад

Was kinda expecting a Laplace transform when I saw that e to the power of negative s in that integral. Though it seems like that method would be messy, if it would even work. ecks dee

@JuanGarcia-ds4sl 2 года назад

an excercise on my complex analysis class involves prooving that the integral from -inf to inf of (e^(ax)/1+e^x) is equal to pi/sin(a*pi) by doing a contour integral with infinite residues, an absolute monster. we still haven't even seen gamma and beta functions so its pretty hard.. ty for the video

@---rp6nq 5 лет назад

I need the explanation of the integration using the Cauchy-Goursat theorem, pleeeeease.

@x15cyberrush9 5 лет назад

umm a request can you make some videos on number theory and algebraic inequalities? btw the videos smexy

@dgrandlapinblanc 4 года назад

Ok. Thank you very much.

@michelkhoury1470 4 года назад

Nice solution. BTW I solved the last integral by using complex analysis but not directly

@ashuthoshbharadwaj6703 5 лет назад

PAPA!~ I tried the same thing when you made the previous video. I used s = x^2 and t= y^2 and changed everything in terms of r and theta. I got till a point papa but I couldn't solve the last single integral( one that appears after e^-(r^2) is substituted between 0 and +infinity CAN YOUHELP ME PAPA

@mrashid5243 5 лет назад

just use e=pi

@ashuthoshbharadwaj6703 5 лет назад

@@mrashid5243 outstanding move!

@michelkhoury1470 4 года назад

Did you calculate the Jacobian?

@Literallyeveryonealive 5 лет назад

I like the edited censors. Much sexy integral, Gg dad

@user-pc9bd9cf2o 4 года назад

at 19:19 why you consider w=t when they are 2 different variables?

@aderinsolajoshua1186 2 года назад

this is very beautify, but risky

@adammaths2920 5 лет назад

Aye! James Grime has blessed this video on 13:05. Seriously that sir is wunderbar!

@neilgerace355 5 лет назад

2:40 or inter outegral

@kairostimeYT 5 лет назад

Hey, now that BPRP and you have resolved all issues, can you guys do something special for this Christmas too? I liked Mathvengers: Infinity War. You guys could do "Math Wars: Rise of the Math Community" or something, this time around. Last time, gotta say, those applications of green's theorem and gauss divergence theorem to prove a very simple integral was mind blowing.

@angelmendez-rivera351 5 лет назад

Harish Madhavan They never resolved their issues. They only agreed to stay away from each other and leave the other alone peacefully

@kairostimeYT 5 лет назад

@@angelmendez-rivera351 oh that's sad.

@subhrajitroy1477 5 лет назад

HOW THE HELL CAN A MAN BE SO COOL????? JUST LOVE YOUR VIDS. PAPA FLAMMY. Can I get a reply?

@Ricocossa1 5 лет назад

6:08 the word you're looking for is probably "tedious" ^^

@alijoueizadeh2896 Год назад

Thank you.

@MrHK1636 5 лет назад

Why didnt't you just plug the formula tau/(1+omega) in omega*s=t and you would have got function for t

@alirezarouhani1289 5 лет назад

I’m not your subscriber nor Peyam’s subscriber, but you do better job than Peyam. My Opinion.

@yaboylemon9578 5 лет назад

Jesus christ, ich liebe dich bruder, gutes math boi 👍🏻

@frozenmoon998 5 лет назад

When the video started and you had a Chinese background, I was like... Damn, is the China TV on or somethin' and I realized, oh yeah, I need to get used to such stuff in this channel. Now I know how engineers feel when they watch your content, papa.

@mickeeyyy 5 лет назад

Love you, papa! ❤️

@joelsagflaatholmberg3922 5 лет назад

Holy fuck

@Polaris_Babylon 5 лет назад

sin(x)=x Not again xd

@u.v.s.5583 5 лет назад

That's the New Testament Formula. Jesus[sin(x)]=(x).

@westgatetv1973 5 лет назад

@@u.v.s.5583 Wait... So Jesus is just arcsin & is only valid for the interval [-pi,pi]? Huh. Neat.

@Polaris_Babylon 5 лет назад

What is Jesus^-1?

@u.v.s.5583 5 лет назад

@@Polaris_Babylon It's the sine. We have sin[Jesus]=Jesus[sin]=Id.

@u.v.s.5583 5 лет назад

@@westgatetv1973 Nope, Jesus is a miracle, you have Jesus[sin(x)]=(x) for all x.

@jimnewton4534 5 лет назад

Hi Papy Flamy, I have an integral question. One way to integrate 1/(x^2 + 1) is as the inverse tangent (x) + C. However, you can factor the denominator into (x+i)(x-i) and use partial fractions to arrive at the (i/2)*(ln(x+i)-ln(x-i)) + C. Are these the same, or is the complex number partial fraction approach just wrong?

@jimnewton4534 5 лет назад

@@PapaFlammy69 by "solve" do you mean "find the roots"?

@dqrksun 2 года назад

Yes, you are correct. In fact that is the complex definition of inverse tangent

@yarooborkowski5999 5 лет назад

Great! When You show derivation of Lagrange inversion theorem?

@yarooborkowski5999 5 лет назад

I am waiting impatiently xD

@marcioamaral7511 5 лет назад

REAL fact! Many engineers are excellent mathematicians don't judge me

@pythagorasaurusrex9853 5 лет назад

Great integration technique! I really enjoyed it. Btw, who needs sleeping drugs and those kinda pills when you can use ayurvedic medicine by calculating brutal integrals :)

@zactron1997 5 лет назад

Man surely that's begging to be a telescoping series? It's not quite, but it's gotta be close haha

@angelmendez-rivera351 5 лет назад

It is not a telescoping series, because z is an arbitrary complex number which excludes the negative integers. For it to be a telescoping series, z has to be a natural number. Even then, though, it still would be due to the -z in the second denominator.

@desertrainfrog1691 Год назад

@@angelmendez-rivera351 erectile dysfunction

@vicktorioalhakim3666 2 года назад

Exercise 10.8 "The Cauchy-Schwarz Master Class" by Steele :)

@MrCoollolman 5 лет назад

Song Name @0:10

@everlastingauraX 5 лет назад

If you break up an integral into two integrals, how were you able to do the substitution to just one of those integrals but not the other if they have the same argument in the integrand? Does it have to do with the different bounds?

@ivan_says_hi 5 лет назад

Why do I watch these videos? Why do I do this to myself?

@Mr_Mundee 6 месяцев назад

why u private the complementary info

@relike868p 5 лет назад

The Chinese is roughly translated as In Hong Kong, something something something

@relike868p 5 лет назад

@@PapaFlammy69 Like I am Hongkongese

@giacomobontempi9112 5 лет назад

"anty-fubiny this shit"

@user-sy2vd3kn2x 5 лет назад

About to become am engineer because in my country there are no jobs for mathematicians and physicists

@user-sy2vd3kn2x 5 лет назад

@@PapaFlammy69 ultra f u c c bro

@dectorey7233 5 лет назад

Great video! Have you thought about doing the laplace transform of tan(ax) and sec(ax)? It applies your sexy Digamma function :D

@masonpiatt2798 5 лет назад

Mfw sinx=x

@u.v.s.5583 5 лет назад

It's just bad asymptotic analysis, you indeed have sin(x)~x, for x

@hammadsirhindi1320 5 лет назад

What is XD?

@matthewvicendese1896 5 лет назад

You drew your integral from the bottom to the top. Is this a satanic method?

@megauser8512 4 года назад

lol

@tomsmith4542 5 лет назад

Nice

@reinerwilhelms-tricarico344 5 лет назад

For that kind of math meth might help. Or perhaps Mäth.

@sorryimactuallynotachef Год назад

you can actually use Ramanujans master theorem backwards to end up with the single integral instead of doing all of the jacobian shit

@tszhanglau5747 5 лет назад

Mfw I know Chinese but don't know what's papa talking about

@tianyouli9762 4 года назад

我开头看得一脸懵逼😂😂😂

@Vincentsgm 5 лет назад

did u steal this distorded friends intro from Podel channel? :v

@Vincentsgm 5 лет назад

ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-AcDvkjug9RY.html@@PapaFlammy69

@gdsfish3214 5 лет назад

@@Vincentsgm I immediately recognized the audio too xd

@gdsfish3214 5 лет назад

@@PapaFlammy69 what I'm actually curious about is how you got that audio if you don't even know who Podel is lol

@gdsfish3214 5 лет назад

@@PapaFlammy69 Makes sense, they know each other and I think pyro sort of adapted a softer version of podels editing style since it was pretty unique and not as overused as the mlg editing back then. Anyways, you should really check out podel since he sort of was the most original editor in my opinion. And I also believe that pyro took some inspiration from him when changing up his style.

@Vincentsgm 5 лет назад

@@gdsfish3214 i see u r a man of culture