If I had a dollar for every time I correctly guessed that the results of these integrals would include the Riemann Zeta function, or the Gamma function, or both, I'd be set for life :)
Ваши видео на ютуб, по части вычисления интегралов - лучшие. Я просто обожаю их смотреть, отдыхая на диване. Знать языка совсем не нужно, весь ход мыслей и так прозрачен, как партия на шахматной доске. Вычисление интегралов, действительно - целое искусство, которое требует глубокого знания и практики высшей математики. Даже в этой задаче, вначале алгебраические манипуляции, потом разложение в ряд 1/(1-x), потом применение знаний по специальным функциям (Гамма и Дзета-функция Римана). Кстати вижу, что вы далеко не первый раз применяете связку таких подходов к вычислению несобственных интегралов.
Спасибо, мой друг. Я рад, что вам нравятся видео. Действительно, решение интегралов - это увлекательный опыт, позволяющий использовать инструменты из различных областей математики.
Duuuude the day of the next cult meeting was getting near and I was going mad deciding which integral I would bring the boys this time, this couldn't have dropped at a better moment
Why can you get away with the convergent geometric series substitution (around 3min mark) without chopping up the integral from 0,1 and 1,inf? Seems like on that first region, exp(-x) tends to be larger than 1.
Great video , for sake of how beautiful \Gamma(5) * \Zeta(4) as the answer is i would just let it be the answer without evaluating it . Just my opinion
Why not improve handwriting skills first, your S can be easily taken as 5(five)? Your mention of the Gamma function must need a separate explanation rather than assuming the learner's depth of unexpected topics such as the Gamma Function or Zeta Function.
Judging by your past interactions with the channel, I can only assume that you're either rage-baiting, or you're genuinely the type of person to stop their Mathematics professor right in the middle of explaining something by saying: "🤓☝️ Achtually, Prof. You forgot to add the dot on the i in the sin!" While being absolutely clueless about what a phase shift is.
If I had a dollar for every time I correctly guessed that the results of these integrals would include the Riemann Zeta function, or the Gamma function, or both, I'd be set for life :)
Ваши видео на ютуб, по части вычисления интегралов - лучшие. Я просто обожаю их смотреть, отдыхая на диване. Знать языка совсем не нужно, весь ход мыслей и так прозрачен, как партия на шахматной доске.
Вычисление интегралов, действительно - целое искусство, которое требует глубокого знания и практики высшей математики. Даже в этой задаче, вначале алгебраические манипуляции, потом разложение в ряд 1/(1-x), потом применение знаний по специальным функциям (Гамма и Дзета-функция Римана). Кстати вижу, что вы далеко не первый раз применяете связку таких подходов к вычислению несобственных интегралов.
Спасибо, мой друг. Я рад, что вам нравятся видео. Действительно, решение интегралов - это увлекательный опыт, позволяющий использовать инструменты из различных областей математики.
idk if you already did this but try doing the integral of ln^n(x)/(x^2 +1) very simple using contor integration it contains pi many times
DUDE!
I JUST MADE A WRITE UP FOR THAT YESTERDAY!
THIS IS SO COOL!!!
That also the nth partial derivatives of the Euler reflection formula if the integral is from 0 to ♾️ or the n power is even
Is it an error at the end ? x to the four rather than x to the s ?
No that's a case I evaluated
Ah something very similar to a blast from the past! keep em up boii!
good solution ,thank you
This is very impressive integral. So, the last integral has x^4 instead of x^s. Thank you for your featured effort.
So sweet I almost cried
Duuuude the day of the next cult meeting was getting near and I was going mad deciding which integral I would bring the boys this time, this couldn't have dropped at a better moment
WOW THAT'S SO COOL
what application do you use to write?
Why can you get away with the convergent geometric series substitution (around 3min mark) without chopping up the integral from 0,1 and 1,inf? Seems like on that first region, exp(-x) tends to be larger than 1.
Nope. It's less than 1 on (0, ♾️)
@@maths_505 Ah, I see my brainfart. I was conflating e^-x with e^(x^-1). Thanks.
Next video is integrating navier stokes equations aha
😂😂
I really enjoyed this one Pakistani boy :)
Great video , for sake of how beautiful \Gamma(5) * \Zeta(4) as the answer is i would just let it be the answer without evaluating it . Just my opinion
Im glad that your pi now is starting to look like a pi and not an x with a hat, but your s always looks like a 5, and here you had both.
I'm afraid that's something that can't be fixed😂
Why not improve handwriting skills first, your S can be easily taken as 5(five)? Your mention of the Gamma function must need a separate explanation rather than assuming the learner's depth of unexpected topics such as the Gamma Function or Zeta Function.
This level of integration i would consider so advanced, that knowledge about these functions can be expected
Bud, he can only explain the integral to you, not understand it for you.
Judging by your past interactions with the channel, I can only assume that you're either rage-baiting, or you're genuinely the type of person to stop their Mathematics professor right in the middle of explaining something by saying:
"🤓☝️ Achtually, Prof. You forgot to add the dot on the i in the sin!"
While being absolutely clueless about what a phase shift is.
Math is a cult
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SUIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII