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 :)

[HansFlamme]

After this brutal Integral, france will surrender

[robinpetersson]

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

Love your vids <3

[gergodenes]

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

[mathma]

I have tried the same brutual integration and ended up getting a infinite series but not the actual 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....

[xcyberrush]

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

[redvel]

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

[gdsfish]

"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.

[JuanGarcia-dssl]

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

[josephholten]

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

[willnewman]

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

[federicovolpe]

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

[---rpnq]

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

[-tv]

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

[adammaths]

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

[michelkhoury]

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

[gregoriousmaths]

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

[ashuthoshbharadwaj]

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

[Ricocossa]

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

[MrHK]

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

[xcyberrush]

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