A ridiculously awesome infinite power tower integral!!!

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Күн бұрын

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This power tower integral was EPIC and the perfect opportunity to introduce the Lambert W function.

Пікірлер: 60

@maths_505 Жыл бұрын

Correction: that's eta(2) at the end of the video. Apologies for the error. Here's the write up for the proof of the reduction formula I used in the video. Don't forget to follow for more awesome write ups on the gram: instagram.com/p/CtpX1B8tIcc/?igshid=MzRlODBiNWFlZA==

@oskarrask9413 Жыл бұрын

#hustle #neverstop :)

@maths_505 Жыл бұрын

@@oskarrask9413 said it before and I'll say it again every f**king time😎😂

@mathalysisworld 10 ай бұрын

Can you prove that integral of lambert W function from 0 to e is e-1 using its infinite series expansion?

@bogdancorobean9270 Жыл бұрын

I'm so glad people still start random math channels and find ways to provide cool content like this.

@jonathan3372 Жыл бұрын

Ah yes, taking the series representation of Lambert W function out of the pocket like it's just another day... (got to confess I never knew there was one in the first place)

@maths_505 Жыл бұрын

I've got deep pockets when it comes to series expansions 😎😂

@pureatheistic Жыл бұрын

Well, what do you carry around in your math pocket on a regular day?

@maths_505 Жыл бұрын

Series expansions, some nice contours to waltz across, the Leibniz rule in case I get bored, the gamma function, its cousin the beta function, its older brother the digamma function and in case the going gets tough, the whole family of polygamma functions and ofcourse some more special functions for special occasions.

@Aditya_196 3 ай бұрын

😂😂 exactly like bro introduces it so casually I feel like it's normal for all the viewers to already know about it

@ves7y775 Жыл бұрын

One word : wow

@manstuckinabox3679 Жыл бұрын

"We're going to invoke the Lambert W function". You're invoking my Vietnam flashbacks of all the implicit solutions to differential equations I could've solved with this function. 6:17 I bet it involves Infinite Series. 6:26 I'M DYING LOL

@maths_505 Жыл бұрын

Bro this comment made my day😂

@robertsandy3794 Жыл бұрын

Awesome result. You make it look so easy. Lambert W is one of BPRP's favourite functions

@alielhajj7769 Жыл бұрын

I kept saying wow every 10 seconds

@western977 Жыл бұрын

Absolutely mind-blowing! 🤯 I just recently discovered your channel. Now I enjoy every video. You are awesome! 😉

@agrajyadav2951 Жыл бұрын

Holy hell that's so cool, how the hell does pi sneak into these things!?

@MrWael1970 Жыл бұрын

Wonderful, it is a magic 😊. Thank you

@gmnotyet 6 ай бұрын

Infinite power, indeed.

@nicogehren6566 Жыл бұрын

very well done

@ProfessorWumbo Жыл бұрын

Wow. This was beautiful.

@btd6vids Жыл бұрын

That was insane

@filipsperl 10 ай бұрын

"Lambert is dead" 😂

@ilmaio 10 ай бұрын

Ouch. It hurted.

@eduardoeller183 Жыл бұрын

Great video!!!

@maths_505 Жыл бұрын

Thanks

@romanvolotov Жыл бұрын

so cool!

@nickruffmath Жыл бұрын

Awesome

@sergten Жыл бұрын

Wow!!!

@Ash.bourne Жыл бұрын

Iam really onto being tricky as u in math , u got any advice or a source i can have the good explanations to what i seek in each genre of math ( like : series , integration , differentiation, and so on .... ) .

@lucidreconalt3229 Жыл бұрын

Yk what Kamaal I'm done this this I've been watching for months and I still cannot solve this differential equation. Can you PLEASE write out the letter u next to the letter n and show me how to differentiate between the 2 of them so that I can finally maybe integrate these techniques into my daily life because right now I CANNOT understand what in the hell you mean when u write lu(x) Anyway much love ❤ :)

@maths_505 Жыл бұрын

Oh that's how we write the natural logarithm on my planet. Sorry I'm still getting accustomed to your earth writings😂

@valdodevirus 10 ай бұрын

Sorry for a dumb question, but IMHO (x^x) ^ (x^x) ^ ... equals to 1 when 0 < x

@hrishikeshaggrawal Жыл бұрын

soo... could you prove the sum in the bazel problem is exactly twice of this power tower?

@aliaujla110 4 ай бұрын

Suppose we remove upper & lower limits.

@grantofat6438 Жыл бұрын

Doesn't the result depend on the value of x?

@zunaidparker Жыл бұрын

Mind boggling that this even has a solution. Does this technique work for the clarification power tower x^x...?

@maths_505 Жыл бұрын

Yeah it should. Only difference I see is getting W(-lnx) as the integrand. The series expansion and integration is then straight forward.

@zunaidparker Жыл бұрын

*classic power tower. Damn swipe typing!

@maths_505 Жыл бұрын

@@zunaidparker it's cool. Better than writing eta(1) right😂. Apologies for that....its been a pretty exhausting day

@oo_rf_oo8824 Жыл бұрын

@@maths_505 isn't that .... exceeds the redius of convergence of the series expansion?

@ekxo1126 Жыл бұрын

I think you have to pay a lot of attention to the convergence of the taylor series of the W function there

@CryToTheAngelz Жыл бұрын

Shouldn't that be eta(2) at the end?

@maths_505 Жыл бұрын

Indeed it is. My apologies

@mikeoffthebox Жыл бұрын

Lambert is dead - long live Lambert!

@padraiggluck2980 Жыл бұрын

Why isn’t ln (x^x)^y = ln (x^xy) = xy ln(x)?

@maths_505 Жыл бұрын

It is but the objective was to get an explicit form for y in terms of x so I only took the y down initially. However you can take the x down too and get the same result.

@Maths_3.1415 Жыл бұрын

Where are you from? Aap kis desh se ho?

@maths_505 Жыл бұрын

Apkey sath waley desh se bro. (This response was also generated by a mysterious AI)

@Maths_3.1415 Жыл бұрын

@@maths_505 I cannot believe you speak hindi (my mother tongue)

@Maths_3.1415 Жыл бұрын

I think you are from America because your accent is just like American's accent

@maths_505 Жыл бұрын

@@Maths_3.1415 nah bro I'm Pakistani and in Lahore, Pakistan.

@Maths_3.1415 Жыл бұрын

@@maths_505but your English is damn nice 😂

@karma_kun9833 Жыл бұрын

300 like

@pureatheistic Жыл бұрын

You proved your great with series, but i didnt see any proof of the first claim of being good with the ladies. Only that your some amount less good with the ladies as you are with series by your own word. I 0refer having as few assumptions in my proofs as possible, so....where the receipts?