A fascinating integral solved using Feynman's technique: int (0,infty) ln(x)/(1+cosh(x))

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@leroyzack265 Ай бұрын

Combining everything to a single argument of a log as ln(π/2exp(gamma)) is pretty damn cool. As you said it was a long day and thanks for entertaining us this evening.

@jmcsquared18 Ай бұрын

We make the same mistakes when we're tired: dropping negative signs and random factors of 2 that are obviously unimportant when we haven't had 8 hours of sleep.

@gonzus1966 Ай бұрын

What an absolutely gorgeous result!

@premdeepkhatri1441 Ай бұрын

I wish I could think fast like Kamal. Thanks for video.

@lokithe.godofmischief Ай бұрын

How do you guys figure out the feynman parameter for such questions? Like are their some known substitution/paramteres for various problem types or is it sheer experience that allows you to figure out the differential part?

@haineshoag3010 Ай бұрын

Whenever you see a lnx that should clue you to use something like x^alpha, because the ln will fall right out when you take the partial derivative. I can’t speak on general substitutions beyond that, though

@mau9639 Ай бұрын

Bro had a long day yet still does pretty good :)))))

@threepointone415 Ай бұрын

I didn't think I needed this before but now I see that I really do

@wowbagger7168 Ай бұрын

Hopefully, your are not too much pestered by our comments like this: "Is the switching of the order of Integration and infiinite sumnation allowed" or "Does this sum converge at the edge of its convergent circle" or "Didn't you miss that Factor of 2 or -1 there and there" 😊

@xanterrx9741 Ай бұрын

Absolutely gorgeous result , thanks for the effort that you take when you are creating these videos for us viewers

@MrWael1970 Ай бұрын

Very cool integral. Thanks for your innovative videos.

@cadmio9413 23 күн бұрын

9:29 My way of justifying the interchange of summation and integration is praying to god that I can, idk abt you

@sachin251998 Ай бұрын

Video showing the value of the Derivative of Eta function at 0 is not in the description

@maths_505 Ай бұрын

Fixed it

@premdeepkhatri1441 Ай бұрын

Thank you for this video.

@CM63_France Ай бұрын

Hi, Still traveling, back soon.

@lokithe.godofmischief Ай бұрын

9:36 "This proof is left as an exercise to the reader" Maths 505 book release spoilers?

@GeoPeron Ай бұрын

Dude found a way around the hyperbolic trig functions problem lol

@daveydd Ай бұрын

Can you try to solve instead this same integral but with cosh(x) in the denominator and ln(1+x²) in the numerator?

@williammartin4416 Ай бұрын

At 7:20 why do/can you switch k to K+1 in order to then change it to k-1

@marcelogutierrez791 Ай бұрын

eta(0) = 1/2 ? Suma of Cesáro?

@insouciantFox Ай бұрын

I feel like an integration by parts leading to int (α-1)x^(α-2)/(1+e^-x) makes things simpler but it all washes out

@AyushRajput-xw2ru Ай бұрын

Hello , mr kamaal can i get a reply from you ?

@Mephisto707 Ай бұрын

For once the gamma constant doesn’t vanish before the end!

@borhenbouchniba Ай бұрын

Great Video and proof but, Is their any new other tricks that we don't know, absolutely yes gut we need to know it for example we know Binome newton formule but we dont know the solution of Polunome of degre "n" !!

@marcellomarianetti1770 Ай бұрын

I'm sorry, is the video about the derivative of the Eta function in the description? I'm probably stupid but I don't find it

@maths_505 Ай бұрын

Fixed it

@marcellomarianetti1770 Ай бұрын

@@maths_505 thanks 👍

@unturnedd Ай бұрын

will there be such case where the integral converges but the switch up of the order of operators is not justified?

@insouciantFox Ай бұрын

Usually it means that you shouldn't be using a series expansion to try to solve the integral, but they do exist. I ran into one once involving 1/1-(e^x²)

@maths_505 Ай бұрын

What were the limits of integration?

@insouciantFox Ай бұрын

@@maths_505 It was such that I would think a GS would be allowed but the exact bounds I can't recall. It was just that as n-> infty the exponential term blew up so I realized I couldn't use that method. Also this was a couple u-subs deep

@maths_505 Ай бұрын

@insouciantFox if it were say from zero to infinity then expanding using e^(-x^2) would have worked for a geometric series expansion but I think the problem you got stuck on is definitely a bit more complicated. If for example the interval of integration had negative numbers as the lower and upper limits a GS would indeed work and maybe a substitution leading something like the incomplete gamma function.