Deriving EULER's INFINITE SINE PRODUCT using the Mittag-Leffler Pole Expansion of the Cotangent!

[@The_Professor_S_]

Mortal Kombat 11’s true final boss: Papa Flammy, The Machine Of Argumentation

[@AA-wq4zy]

In math forums,the expression is always said to be derived from Weierstrass factorization theorem, but this is a new and different way to prove this ,thanks!

[@twistedsector]

sin x / x = x / x = 1 ez

[@deusvult5738]

Filth

[@nicholasheilig3694]

It's actually holds because x tends towards 0 and you are allowed to approximate sinx for small angles

[@helloitsme7553]

From this identity you can also easily see that the limit as x->0 of sinx / x is 1 when you divide both sides by x. And yes that's allowed cause you're taking the limit

[@ianmathwiz7]

"...but I actually prefer the rigorous approach a bit more." And with that, Papa Flammy declared war against the physicist camp.

[@frozenmoon998]

The infinite boys laughing at the beginning really got me. You know papa flammy gonna make some infinite joke for ye, before the actual fun begins.

[@rabindranathghosh31]

Wow this identity is so useful in showing that sin(x)≈x for small values of x

[@oswinheinrich3709]

Proposal for discussion: what do you get when you replace the minus by a plus in the infinite product. Isn't it sinh(x), but how goes the proof?

[@tomkerruish2982]

Use sin(ix) = i sinh(x).

[@gregoryfenn1462]

'whale... cumback' I was not expecting this kind of joke on a maths lecture :O

[@wiloux]

"teH IntEgeRaAl" xd

[@kevinfung6697]

Engineers : “sinx=x.”

[@typo691]

x=x+1

[@neilgerace355]

And cot x = cos x / sin x = 1 / x

[@felixmendelssohn8814]

It does for small angles my friend

[@MooshPeriwinkle]

Hi Flammy! Got a little question at time stamp 7:36, what functional equation are you talking about in complex numbers that allows us to make the switch from series to product? Doing a lil complex analysis project and this would be so useful.

[@jonafladerer3074]

Oiler would have been proud papa!

[@danielcastillo2299]

What a perfect segue into fractional calculus!!!

[@user-wu8yq1rb9t]

Dear Papa ... At that time you were sick but you did your best as always. Great video with interesting results (combine it with previous video, cot). Thank you so much 💖

[@maxteer2800]

swear i'm not the only one who feels this, but you are my spirit animal

[@insert_a_good_name_here4585]

3:52 small angle approximation?

[@insert_a_good_name_here4585]

@@PapaFlammy69 as someone who has no idea what's happening (most of the time, through no fault of your own) I'm just happy to recognise a good friend.

[@akshat9282]

your eyes look really messed up. I know this was recorded a while ago but are you okay daddy? you don't have to stress yourself out so much to put out videos

[@mattgsm]

He's up all night figuring out the proof to write in the margin.

[@akshat9282]

@@mattgsm or just figuring out where to put euleroids in his videos

[@SchrondingersCat]

Wow. Your final solution to the chalk question seems a bit cold to me...

[@amanr4708]

We need some physics too papa!

[@49fa75]

@Cosmic Rift Just read some Michio Kaku or Brian Greene 🤣 (if you know what I mean)

That was damn exciting ! Btw ... that chalk has no right to exist on this planet any more ... Hmm, is it a spoiler to have a video from another planet next time? :-O Good vacation plan btw ... another planet.

[@Davquest]

Microphone: *rubs agains shirt* Literally everyone: NANI?!

[@hungryfareasternslav1823]

Engineers: sin x = x Newton: *Throws trillions of apples at engineers* Leibniz: Newton, Isaac, you are noob. *Cut all engineers with his integral sword* Newton: What!!!

[@Exilelord5678]

This was so amusing to watch, you should have a *Maxmoefoe* meltdown in one of your videos

[@toaj868]

Wouldn't evaluating lim_x->0_sin(x)/x using Taylor series be circular logic?

[@YorangeJuice]

No, he’s deriving the infinite product for sine, not the infinite sum/taylor series for sine in this video

[@toaj868]

@@YorangeJuice What I meant at the time was that in order to derive the Taylor Series one needs the derivative of sin(x) and for that the limit_x->0_sin(x)/x which makes 4:12 circular but I have since realised that he could be using an alternate definition of sin(x) where the limit is derived via the Taylor Series.

[@Vincentsgm]

2:28 i've spit my imaginary coffee cus laughing

[@Frostbitecgi]

this video is amazing

[@tiagomrns]

that's the factorization of a infinite polynomial with zeros on k*pi, k being an integer

[@swordslash8]

I dunno why this was recommended to me but I enjoyed it

[@lionelronaldo1574]

Bro you looks very handsome

[@josephholten5088]

Papa, as always great vid, just try to keep your mic from rustling :)

[@pedromedeiros7469]

Stats ain't math

[@chaitanyavarma1747]

Damm flammy boy

[@peterclark5244]

Do you take submissions?

[@peterclark5244]

integral from 0 to 2pi of cos(x)/(1+cos^2(x))

[@duggydo]

My shorties are always quite exciting!

[@dectorey7233]

6:20 TOP 10 MOMENTS RIGHT BEFORE DISASTER

[@jamesbra4410]

DO MORE FUNCTIONAL ANALYSIS!!!

[@tomatrix7525]

Daddy euler.....more like daddy flammyyyyyyyyyyy

[@mrandersonpw53]

Me after a terrible complex quiz: dude I couldn't get the branches of tan(z)=z. I suck. I'll watch KZbin to recover my self-esteem having fun. Papa flammy: We are about to demostrate the euler product formula of sen, using log and cot. Me: you fuc...ing genius, son of the bit.... True history 😂

[@MaxxTosh]

Is seriously nobody going to call out the whalecum thing? Damn

[@coefficient1359]

OP flamming boi

[@nevokrien95]

Chalange try and get an aproximation for how many prime factors a number has

[@TheNachoesuncapo]

good luck in your vacation to paris pappa,but i would advice you not to visit notre dame this time

[@remlatzargonix1329]

Bravo!

[@IshaaqNewton]

When I came to this video to get the proof and found that I have to see another video before this... Flammy: We just have to substract 1/z from both side Me: I'mma Outta Head :o

[@WhattheHectogon]

Hey Papa, trying to get my own math channel going. What microphone and camera do you use, and would you recommend them? Cheers! Love the videos

[@armandobuzzini9171]

Wow, the best

[@morbidmanatee5550]

Weirstrauss theorem in action

[@nevokrien95]

Cool

[@herlanggaizul6965]

Where TF you get the spell of INTÉGÉRAL ? 😂🤣 Its really funny

[@everlastingauraX]

5:40 This is worst than someone spoiling the Avengers movie :(

[@borisbryant.007]

free speech lecturer "fucking bloody" i think like this guy

[@MarcosGarcia-kk8lc]

You looked fukked up papa, guess you are better now. Also, I never encountered this identity before, Im an engineer so thats probably why, fml.

[@douro20]

I would had taken the chalk to hydrochloric acid.

[@digvijaygadhavi7418]

Waiting for avengers endgame integral war collaboration.

[@אלעדערוסי-צ4ד]

Boiii

[@borisbryant.007]

loud reading helps with speech mathematical texts don't "flow" read a philosophy or something

[@martincaputo2361]

Early asf boiiiiiiiii

[@peregee]

bruh

[@Gameboygenius]

sqrt(g) tho

[@rome8726]

Gucci☺

[@marc627]

get out of my browser history, if you are so kind. I just finished watching your video, switched to the next tab on my browser (Wallis product wikipedia entry), and I there it is: Euler's fucking infinite product for the sine. PD: I am not gonna call you daddy. Thanks, btw.

[@pranayvenkatesh8815]

Notification squad

[@jony7779]

integehRAHL

[@PapaFlammy69]

:D

[@GrandMoffTarkinsTeaDispenser]

I will sue you for what you did with Tom Cruise to the faces of Euler and Gauss.

[@deusvult5738]

OwOwOwOwOwOoooooooooooO

[@Khushal435]

Bro your writing on board is not clear...

[@sylowlover]

Please don't use the r word :

[@sylowlover]

:(

[@QuoteVG]

You should stop using those fucked up letters in your title because I can't see them on mobile

[@hoodedR]

Rip english

[@iainfulton3781]

It's pretty damn quite easy

[@armandobuzzini9171]

Wow, the best