Lagrange Inversion is wild

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Today I present the Lagrange Inversion Theorem to you. Not going to prove it though, just applying it to solve a simple polynomial equation :) Enjoy! =D
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[@PapaFlammy69]

*_Thanks for watching my dear flammily members

[@oni8337]

nice another epic lagrange inversion theorem video

[@anshulrai677]

Nice FlammyBabaOP

[@christianpaul3651]

I weiss grad net mer wo I mein Schwonz reinstecka soll ...

[@galactusthehungry2681]

another epic video, do you know where I could find the proof? I can't seem to find it anywhere online?

[@AndrewDotsonvideos]

What’s the theorem? I mean if it’s in physics, it’s invertible, QED.

[@oni8337]

lol

[@AndrewDotsonvideos]

@Kiko Frías Tenza good question. As it turns out, only 4x7 matrices leave the monoidal functor invariant under conformal diffeomorphisms, not to be confused with generators of the poincare unitarity condition.

[@houseflyer4014]

@@AndrewDotsonvideos *nodding my head pretending to understand*

[@user_2793]

Yeah lol, when dealing with canonical transformations and generating functions, we have to assume so much invertibility.

[@AndrewDotsonvideos]

@@houseflyer4014 What I just said was udder nonsense btw.

[@ShortHax]

When Pappy Flammy says something is gonna be wild, your brain is gonna be in for a tough ride

[@PapaFlammy69]

we'll see, we'll see

[@anshumanagrawal346]

Bet

[@abdullahfehratbegovic2623]

a wild Shorthax outside its natural habitat

[@j.r.8176]

"Lube up your brain!"

[@hxc7273]

I'm so glad we had this theorem or I never would've been able to solve that equation.

[@alxjones]

Worth pointing out that the series is only guaranteed to have non-zero radius of convergence, i.e. convergence in a neighborhood of f(x_0), and so it doesn't necessarily solve all equations outright. Of course, this is obvious in the sense that f may not be invertible, and certain invertible subdomains may not contain a root. For example, x^3 - 3x + 3 has no roots on (-1,1), so if you chose an x_0 in that interval, your inverse series will not converge at y = 0. However, if you have a decent guess of the root or know that the function is invertible, this method works nicely.

[@angelmendez-rivera351]

One good and important application of this theorem is to solve quintic equations. Quintic equations cannot be solved using radical functions in general, but they can always be transformed into an equation of the form ζ^5 + ζ + a = 0. By having ζ^5 + ζ = -a, one can use the Lagrange inversion theorem and obtained the solutions to the equation for every complex a. This is used in the definition of the Bring radical, which is an algebraic function that cannot be formed from compositions of radicals and rational functions. In general, this can always be used for any polynomial equation, which helps rather significantly with studying algebraic functions in spite of the Abel-Ruffini theorem.

[@GiornoYoshikage]

Today I remembered there's something about the theorem in Knuth's "The Art of Programming", checked this, and now I see your video with same subject! What a coincidence!

[@MathAdam]

I'll save everyone 18 minutes. The answer is 3. (It took me only 10 minutes to figure it out.)

[@MeMyselfForWho]

buzzkill

[@nullplan01]

The journey is the destination.

[@PlasmaFuzer]

Awesome video. You know this was also how I introduced solving linear equations in the Introductory Algebra course I was teaching at my local high school. For some reason, the students had a hard time grasping something so straightforward. I guess I forgot to recommend they bone up on Cauchy's residue theorem and the analyticity of functions before the first day. Oops.

[@PapaFlammy69]

smh

[@jaykane42]

I'm currently learning linear algebra - about to move onto calc 3 when I'm done -. So, I don't fully understand what I've seen in this video. But, of what I do understand, you explained it really well and I found it very interesting! Thanks for making such awesome content and I hope you have a lovely day!

[@PapaFlammy69]

Have a great day too, Jay

[@redpepper74]

Currently doing pre-calc, so I don’t -fully- understand what’s going on here but I _was_ able to use the formula to figure out that when 3x = 6, x = 2. Wild

[@benjamingurevitch4097]

@@redpepper74 I'm also currently doing pre-calc and plan to use this on one of my tests to troll my teacher lol

[@timothyaugustine7093]

5:55 When the chalk hits hard on a bracket with the word "OF" you know the stuff that comes next is bussin'.

[@phyarth8082]

0:07 Very good meme dude (thumbs up) It is also circular thinking firs number connected with last one in the sequence of numbers 1+100+2+99+3+98+4+97+5+96+... Analytical continuation 1+2+3+4+5+..+infinity=-1/12. Clock has 12 arrows it is also circular summation of mod(12). In every country we hear Gauss fable in Math class, even it has not historian evidence of existence.

[@yoav613]

It is great to learn new math theorem! I think you should make a series of videoes in this inversion theorem you explained it well

[@goodplacetostop2973]

17:25 Ending 17:33 Real ending

[@houseflyer4014]

I see you have blessed the flamily with your presence. Send our regards to Michael Penn 😁

[@maxwellsequation4887]

Ooooo

[@FloThePro1231]

one of the best videos for a long time, great new topic and learned new way to solve stuff, thank you

[@PapaFlammy69]

[@CallOFDutyMVP666]

Thanks for the knowledge Pappa Flammy! I learned something new every video. Greetings from American

[@PapaFlammy69]

[@乔峯]

Dear sir, could you show us how to derive this Lagrange Inversion Formula? I am unable find it on the website. Thanks & regards.

[@alexismiller2349]

Lol everytime I learn something, it shows up on your channel in the same week, I swear it's a curse

[@PapaFlammy69]

xD

[@pinklinecabs3967]

Yeee watching papa flammy while doing math homework.

[@fakharyarkhan5848]

This is pretty cool but what happens if you try to use this on a general quintic polynomial? Would it be impossible to determine what the summation converges to since you can't have a generalized, explicit solution for the quintic polynomial?

[@PiR2InTheUSA]

I don't think it will be a generalized expression since it's evaluated at a specific point.

[@angelmendez-rivera351]

An explicit formula for the roots of a quintic polynomial function does exist. This formula just cannot be written using addition, multiplication, and radical functions alone. You can, however, use the Lagrange inversion theorem, and use the generalized hypergeometric function to express the roots.

[@subhasishguha571]

I'm a physics student, I watched to the end to listen to how he said Lagrange

[@sharpnova2]

Physics and Math Lectures has a two video series that covers the Lagrange Inversion Theorem and uses it to get a Taylor series for W. Love your channel bruh but I think Physics and Math Lectures's was a bit cleaner on this topic.

[@tonaxysam]

I like the "wa~" pronunciation for y

[@nikhilkenvetil1594]

That meme in the beginning was wild

[@Idk-hp3oo]

14:46 yes papa im interested in Algebruh

[@PapaFlammy69]

nice.

[@iplaygrangemusic]

papa flammy killin' it

[@zh84]

Was it pouring with rain when you filmed this?

[@integralboi2900]

You lost me at 5:50. I still like these unreasonable ways to deal with simple problem.

[@gdineshnathan]

I was expecting a proof of the theorem, anyways great video. Something new!

[@PapaFlammy69]

=)

[@soheirmrain975]

hi thanks for your explanation but i have this equation and i don't know how can i solve it ...... 2*cos(x) - beta*sin(x) + beta*sin(alpha*x) = 0 alpha and beta are two parameters and i need to solve x x=f(alpha,beta)

[@humanbeing1213]

Another awesome video!!!

[@themightyripples6582]

This is so good, thank you, to be vague, lol. I wish i could like 3 times.

[@nikhilnagaria2672]

0:04 that meme tho

[@syedinayat3548]

LIT GOT mE

[@JanxakaJX]

Papa you've been hitting the gym harder than my dad hits me! :D

[@PapaFlammy69]

not really lol, I hate working out

[@redpepper74]

Considering flammy’s reply, it’s good to know your dad doesn’t beat you

[@Eigenbros]

That was pretty sweet 👌

[@MeMyselfForWho]

Can you do that for polynomials on both sides?

[@juijani4445]

0:05 -gaud- -gamer- Gauss tier mim

[@InfiniteQuest86]

Do you think if I teach my 9th grader to reproduce this in Algebra 1 when they get this problem, he would get full credit?

[@PapaFlammy69]

yeye, he definitely should tbh

[@InfiniteQuest86]

@@PapaFlammy69 Yeah sometimes helping with homework can be a little annoying for him. Your teacher only said that's true because you are working in a field. And dang I remember when multiplication was guaranteed to be commutative. Must be nice. lol

[@muskyoxes]

The sliding boards made me seasick in part of this

[@PapaFlammy69]

oh man xD

[@esraatamdede5550]

You look tired are ok @Flammable Maths

[@PapaFlammy69]

yeye, just working a bit too much all day long hehe ^^

[@danielkirilov8065]

Shiii, next time imma blow my professor's mind!!

[@tszhanglau5747]

you can say it's lit this video in a nutshell:everything vanishes but the solution

[@Zavstar]

I only watch the videos for the memes at the start

[@synesthesia2896]

I lost track of things in the first 6 minutes, but nice video anyway

[@glory6998]

Plz teach calculus of variations ....🐸

[@someperson9052]

This video has been out for 15 minutes and it already has a dislike. Somebody is subscribed to this channel just so they can immediately dislike. Wtf

[@someperson9052]

And there are dislikes on every video. I wanna meet these people just to see if they exist

[@PapaFlammy69]

yup, always on time. Someone always dislikes approx. 15- 30min after release lol

[@sharpman5772]

ppl with tiny pp be like

[@someperson9052]

@@sharpman5772 big fax

[@angelmendez-rivera351]

@@PapaFlammy69 Maybe it's a bot. I doubt any human being can actually be that consistent without help from technology. Or maybe I'm underestimating humans.

[@YitzharVered]

Best papa

[@mudkip_btw]

Oh yes I was looking forward to this one! Time to become a real man lol

[@mudkip_btw]

ah yes, Lagronch

[@hardikjoshi8557]

Inverse of Lagrange is Gauss😌

[@luggepytt]

No, it's egnargaL

[@powotode3252]

Yep, I'm lost

[@advaykumar9726]

Has anyone watched mathologers video yet?

[@PapaFlammy69]

ye

[@Chemasaurus]

Fuck, if I had a child in some intro math I'd make them write this for an answer

[@PapaFlammy69]

:DDD

[@benjamingurevitch4097]

That's what I'm gonna do in my precalc class lol

[@meowwwww6350]

Yeah I'm eight

[@JuanGarcia-ds4sl]

x-1=2 => x=3 *khaby lame comes in*

[@tobybartels8426]

You're doing too much work here. First you check that it's analytic by finding the Taylor series, then you check that the derivative is non-zero by calculating the derivative. You only need to do one of these! If you can calculate the (complex) derivative, then it's analytic, no need for the Taylor series. Conversely, if you have the Taylor series, then the linear coefficient in the series is the derivative, no need to differentiate it. You're really putting yourself through a lot of extra work for no good reason!

[@PixelSergey]

okay papa very epic now show us how to get something useful 😠🔫

[@nikhilnagaria2672]

Fugacity

[@caseyhokanson1844]

Yeah I’m second

[@caseyhokanson1844]

Yeah I got a heart

[@adnann5232]

@@caseyhokanson1844 Yeah I Replied

[@caseyhokanson1844]

Yeah got a reply

[@nikhilnagaria2672]

@@caseyhokanson1844 got a reply to a reply

[@rialtho_the_magnificent]

do I hear a robot vacuum in the background rooming your room?

[@PapaFlammy69]

That was my wife lol

[@nikhilnagaria2672]

@@PapaFlammy69 😳

[@adnann5232]

Yeah I'm first

[@dizzyd7315]

I know a much easier way of solving this equation lol

[@GammaFZ]

nah this is the most easiest and straightforward, are you denying lagrange's ingenious theorem? He's one of the math GOATs. You should publish your research on arxiv or smth