Can We Solve A Transcendental Equation 😁

[@Dave61Mi]

“Analytically”?

[@scottleung9587]

Yeah, I think that's the word he was looking for.

[@SyberMath]

Yesss! Thank you 😍❤️

[@scp3178]

No, the right word is arithmetically. Americans always say algebra, when they actually mean arithmetic. Algebra id not „2x-17=3x“! This is arithmetic. Algebra is about groups, fields, rings etc

[@GourangaPL]

That also prooves that Lambert's W function isn't odd, because if it was then -W(1/e) would be equal to W(-1/e) = W[ (-1)e^(-1) ] = -1 which is not true here since that would give us the result of -2

[@leif1075]

But again don't you agree lambert is a contrived cheat which doesn't tell you the ACTUAL VALUE of the answer..and it's not something anyone would think of no way no how no matter how smart you are. So why use it. Curious how or why anyone would disagree.

[@emanuellandeholm5657]

Another nice problem is finding the inverse of y = x + e^x. Yes, it involves Lambert's W

[@ben_adel3437]

Is it x-w(e^x)=y

[@emanuellandeholm5657]

@@ben_adel3437 That's the implicit form of the inverse. Keep at it and you will find an explicit formula involving Lambert's W

[@TejasDhuri-p8z]

I solved using Newton Raphson method. Required three iterations to get x=-1.2784

[@leif1075]

That's just an approximate value right?

[@TejasDhuri-p8z]

@leif1075 it gives correct value upto 3 to 4 correct decimal places

[@worldnotworld]

I dislike Lambert's W function. I don't like how it sits there irreducibly. I guess I have to respect it, but I do so only grudgingly.

[@leif1075]

Becauseyou agree with me it's a contrived cheat right?

[@Petervannederland]

ever since i learned about the witchcraft called "series inversion" i have visions of expanding functions in a taylor series and then inversing the damm series

[@maxwellarregui814]

Buenos días Señores: SyberMath. Reciban un cordial saludo. Gracias, es un buen video. Éxitos.

[@SyberMath]

¡Gracias por sus amables palabras! 😍

[@perkin524]

How do you evaluate a LambertW function? Can you look it up tables? I'm 84 by the way!

[@SyberMath]

Wow! That's amazing!!! Glad to hear that. 😍 You can use an online calculator like Wolfram Alpha or look at the graph and estimate: www.desmos.com/calculator/uz8hvr526h Basically, finding W(1/e) means solving for y in the following equation: ye^y = 1/e (look at the y value of the intersection point on the graph - that's W(1/e))

[@scottleung9587]

Nice!

[@SyberMath]

Thanks!

[@crimfan]

Math internet's favorite function.

[@yuyuvybz]

Internet's favorite math function

[@malvoliosf]

Well, at the end, you didn’t solve it analytically. You analyzed it to a Lambert-W, and got that numerically.

[@jieyuenlee1758]

e^x=-(x+1) e^(x+1)=-(x+1)e e^-1=-(x+1)e^-(x+1) W(e^-1)=-x-1 x=-W(e^-1)-1

[@giuseppemalaguti435]

x=-W(1/e)-1=-1,27846

[@pnachtwey]

Yotube has too many channels that solve weird function that NEVER appear in reality. Show me where this functin woulld be use. Also, I would just plug the formula into a CAS and solve it numerically or symbolically. Then I could concentrate on the application.

[@SyberMath]

The usefulness is not important. The video should be as weird as possible and pique interest. The weirder, the better. That's how the algorithm works and that's why you see a lot of faces with a shocked/weird expression on thumbnails and click-baity titles like "Harvard Entrance Exam" for a problem like 1ˣ = 2. People want to be entertained! They click out of curiosity.

[@SteelBB9]

As usual thank newton lol

[@SweetSorrow777]

Of course, Lambert W function.

[@neuralwarp]

You wanted an algebraic solution. You can't use Lambert's W function.

[@syndrrgd812]

That's not possible, e is transcendental

[@s1ng23m4n]

W-function no thanx go next

[@SyberMath]

😲🤪😁

[@barakathaider6333]

👍

[@alexchan4226]

1

[@leif1075]

Lambert is a CHEST..so whybuse it..doesnt everyone agree with me. It's contrived abd doesnt require intelligence or ingenuity. Hope you can respond Syber. Don't mean to be rude nust the truth. Thanks for sharing.