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Calculating one BRUTAL Integral! Deriving Euler's Reflection Formula the RIDICULOUS way!
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- Опубліковано 3 лип 2019
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Refl Formula: • Euler's Reflection For...
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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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![So good!: ONE Integral, TWO Solutions! [ Desmos and WA Insights included ]](http://i.ytimg.com/vi/hAxdnNwjsTo/mqdefault.jpg)
After this brutal Integral, france will surrender
@@PapaFlammy69 ❤️
You misspelled. It's called Wheeler's Reflection Formula ;)
Love your vids
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
I know right!
"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.
man those Chinese things got me
you're a real meme lord😂😂😂😂😂😂😂
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....
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
great video flammy! i love these kind of videos. because o this kind of content i've loved your channel
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
Good video. I am glad you are sticking with math content on your channel
Lmaoooooo that intro I love the Chinese part of ur vids
Please bring it back
:D
Nice solution. BTW I solved the last integral by using complex analysis but not directly
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
I need the explanation of the integration using the Cauchy-Goursat theorem, pleeeeease.
this is very beautify, but risky
2:40 or inter outegral
umm a request
can you make some videos on number theory and algebraic inequalities?
btw the videos smexy
Ok. Thank you very much.
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
just use e=pi
@@mrashid5243 outstanding move!
Did you calculate the Jacobian?
Thank you.
6:08 the word you're looking for is probably "tedious" ^^
at 19:19 why you consider w=t when they are 2 different variables?
Aye! James Grime has blessed this video on 13:05. Seriously that sir is wunderbar!
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.
Harish Madhavan They never resolved their issues. They only agreed to stay away from each other and leave the other alone peacefully
@@angelmendez-rivera351 oh that's sad.
Why didnt't you just plug the formula tau/(1+omega) in omega*s=t and you would have got function for t
Love you, papa! ❤️
Jesus christ, ich liebe dich bruder, gutes math boi 👍🏻
sin(x)=x
Not again xd
That's the New Testament Formula. Jesus[sin(x)]=(x).
@@u.v.s.5583 Wait... So Jesus is just arcsin & is only valid for the interval [-pi,pi]? Huh. Neat.
What is Jesus^-1?
@@Polaris_Babylon It's the sine. We have sin[Jesus]=Jesus[sin]=Id.
@@westgatetv1973 Nope, Jesus is a miracle, you have Jesus[sin(x)]=(x) for all x.
HOW THE HELL CAN A MAN BE SO COOL????? JUST LOVE YOUR VIDS. PAPA FLAMMY.
Can I get a reply?
I like the edited censors. Much sexy integral, Gg dad
I’m not your subscriber nor Peyam’s subscriber, but you do better job than Peyam. My Opinion.
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.
Song Name @0:10
Holy fuck
REAL fact! Many engineers are excellent mathematicians
don't judge me
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?
@@PapaFlammy69 by "solve" do you mean "find the roots"?
Yes, you are correct. In fact that is the complex definition of inverse tangent
Exercise 10.8 "The Cauchy-Schwarz Master Class" by Steele :)
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 :)
Great! When You show derivation of Lagrange inversion theorem?
I am waiting impatiently xD
Man surely that's begging to be a telescoping series? It's not quite, but it's gotta be close haha
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.
@@angelmendez-rivera351 erectile dysfunction
why u private the complementary info
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?
"anty-fubiny this shit"
Why do I watch these videos? Why do I do this to myself?
Mfw sinx=x
It's just bad asymptotic analysis, you indeed have sin(x)~x, for x
The Chinese is roughly translated as In Hong Kong, something something something
@@PapaFlammy69 Like I am Hongkongese
You drew your integral from the bottom to the top. Is this a satanic method?
lol
Great video! Have you thought about doing the laplace transform of tan(ax) and sec(ax)? It applies your sexy Digamma function :D
What is XD?
About to become am engineer because in my country there are no jobs for mathematicians and physicists
@@PapaFlammy69 ultra f u c c bro
For that kind of math meth might help. Or perhaps Mäth.
Nice
you can actually use Ramanujans master theorem backwards to end up with the single integral instead of doing all of the jacobian shit
Mfw I know Chinese but don't know what's papa talking about
did u steal this distorded friends intro from Podel channel? :v
ua-cam.com/video/AcDvkjug9RY/v-deo.html@@PapaFlammy69
@@Vincentsgm I immediately recognized the audio too xd
@@PapaFlammy69 what I'm actually curious about is how you got that audio if you don't even know who Podel is lol
@@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.
@@gdsfish3214 i see u r a man of culture
我开头看得一脸懵逼😂😂😂
Topology > Analytic number theory.
FIRST