A mesmerizing result
Вставка
- Опубліковано 17 чер 2024
- A beautiful iterated integral with full solution development leading to a closed form with this awesome linear combination of zeta functions.
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Bro had a football fan moment before proceeding to jump to an integral
You're something special
Ohhhkaaay cool!
If we make it a triple integral with the same structure you will get two additional zetas and and additional -2, the generalization is pretty cool and I think the limit as we increase the dimension of integration is convergent and it is actually equal to -1 + the sum from n=2 to infinity of zeta(n)-1 !!! Really cool and worth investigating
Hi,
"ok, cool" : 1:55 , 5:24 , 8:03 , 8:43 ,
"terribly sorry about that" : 2:05 , 2:44 , 4:34 , 8:20 , 9:35 .
The final results with ascending coefficients of zeta is really cool. "We enjoyed the video. Thank you see you next time". Oops I'm using some one's words.
No wonder you are a sigma with this talent you have when it comes to solving these kinds of integrals. I hope I will someday become as good as you, meanwhile, keep up this amazing work :)
Thank you very much.
Cool result
Sport and math perfect!😊💯
Logarithms
Logarithms
Logarithms
@@arkadelik Logarithms
Logarithms
Logarithms
Sir you are a poet
Perfect
Hope to learn about Zeta fn. of odd powers apart from Euler's even powers. He loved using ln. to "lessen the labor".
bro rest well bro
i think you pulled an all nighter to watch football.
2:13
Have you seen the new Oppen-adder movie?
"Now I have become the sigma, the summator of the series."😅😁
Nah haven't seen that one but damn that was cool 😂
May I ask what app you use for your videos?
Please integrate x^a*cosnx*e^(-kx)
Can this be extrapolated out with more integrals? Like integral over unit cube of lnx*lny*lnz*ln(1-xyz) being (guessing result if it continues as before) eta2 +eta3 + eta4+ eta5 - 5? Or generally N Integrals_01 of Product(ln(x_n), 1, N) = Sum(eta(n), 2, n+1) - (n+1)? (I probably fucked up some notation there, but hopefully what I mean is understood.)
On notation: zeta, not eta.
On the concept: seems worth exploring!
I was wondering the same. If its the case then Its can give some insight on Zeta and its distribution.
Oh yeah it's definitely gonna carry over thanks to symmetry.
I tried to find a solution to the general integral:
∫...∫ln(x1)•...•ln(xN)•ln(1-x1x2...xN)dxN... dx1 (with all the integrals going from 0 to 1) and got this:
I = -2N + sum{j=2 to 2N}Zeta(j)
I looked at numerical answers for these integrals, and it seems there is a factor of -1 multiplied for each n for the solution you provided@@lizardwithahat4862
Greetings from the Czech Republic.
Greetings
@@maths_505 I knew there was something weird with my comment 🤣🤣🤣
Sweet result.
I=-Σ1/((k+1)(k+2)^4)...poi bisognerebbe sintetizzare con zeta function..
Who you got for the Copa?
Also I dare you to use ξ as a variable
Argentina
2:13 Kamaal your sigma dad joke literally sent me hysterically laughing across the house. I have to thank the Gods i am home alone right now.
Ive never been more comedically t-boned before in my life 😂
portugal played well but they porbbaly won't win the whole thing - my guess is a quarter final exit
I thought we're gonna find the value of zeta2 zeta3 zeta 4😂