UNBELIEVABLE calculus result using Feynman integration

Definitely one of the most beautiful results ever published!
Important derivatives of the gamma function:
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Integral for η'(1):
• ONE OF THE COOLEST INT...
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[@maths_505]

Derivatives of the eta and zeta functions at zero:
th-cam.com/video/DiLo9i6Io0M/w-d-xo.html

[@darkchocospy7080]

bros pullout game is crazy

[@maths_505]

Which is why I've never had to get up in the middle of the night to go out and buy milk

[@insouciantFox]

Feynman's trick is a valuable trick to have...
In mathematics as well

[@maths_505]

😂😂😂

[@dariuszpanchyrz2784]

What can I say. The most creative and the best math channel on the yt. Respect and regards.

[@YahontAction]

Я не знаю английского языка, я 25 лет назад учил высшую математику и занимаюсь совсем другими делами, я смотрю этот ролик вообще без звука. И мне все понятно! Как бывший фанат интегрального исчисления, жму руку - фанату действующему!!!

[@EIswazi]

You can simplify the ln^2(2) even further by writing it as ln(2)ln(2) and then applying properties of logarithms to yield ln(2^ln(2)). Then you can combine all of the logarithms and bring in the 1/2 to make the whole thing just the argument of one logarithm and it looks so cool imo.

[@kaanetsu1623]

Amazing!! Pls bring derivative of dirchelet eta of zero video

[@MrWael1970]

Really awesome. This is very smart. Thank you

[@GeoPeron]

I understand that a lot of dx's were missed through the videos on this channel... but I don't think writing two of them in one integral is how you pay it back 🤔😅 2:17
also nice explanation, very elegant solution

[@timemasterdm2462]

2:17 AYO‽

[@definitelynottigerwhitten5865]

I was not expecting that😂

[@nizogos]

The substitution which leads to the use of the gamma function can be avoided if we view the integral as the laplace transform of L{x^(s-1)}(t) evaluated at t=(k+1)

[@absxn]

jeeeeeeeeeeeeez nice one👌

[@jameyatesmauriat6116]

Can you please refer us to these freightening basics for these advanced integration techniques? What is eta function? Is it related to Dirichlet?

[@roykamaan3357]

Forgot 1/2 at the for the (lynx)^2. Thank you for the integrals

[@bartekabuz855]

how do you come up with those integrals?

[@maths_505]

That's easy.....making mistakes while solving other integrals

[@bartekabuz855]

chicken egg problem?@@maths_505

[@SuperSilver316]

Or do the problem in such an insane way that you just generate more integrals from the target integral.

[@maths_505]

Oh yeah I've tried that too

[@morveman_yt9567]

Another incredible integral… just a question I tried to find the value of the sum as k goes from 1 to infinity of k^-k but never got the result if anyone knows…

[@maths_505]

It doesn't converge to a nice closed form

[@morveman_yt9567]

@@maths_505 oh that’s maybe why I couldn’t find one… thanks !!!

[@insouciantFox]

I know it's the same as the integral from 0 to 1 of x^-x

[@shivanshnigam4015]

Hey can we do this using the Feynman Technique
Integral from 0 to 1 of ((e^-x)-1)/x
Or this integral is just not doable

[@The_Shrike]

Hey man, I think I posted the same comment on another vid, but still wanted to see if anything could be done about it. I watch all of your videos from my phone, and recently I have been unable to view it fullscreen since a bunch of the work gets cut off. It may be an issue from my end, but this only started happening recently (maybe you started doing these on a different device), and it’s quite difficult to watch it vertically. Could you check things out in your end by any chance? Thanks

[@jameyatesmauriat6116]

Where is Feynman trick in the solution?

[@ranjithkumararunachalam3844]

How partial differentiation works?
Can we integrate partially?

[@insouciantFox]

Partial differentiation is the same as normal diff. except you treat all other parameters as constant. Total diff. (with upright d/dx) of a parameter involves the use of the chain rule.
Technically you do integrate partially whenever you integrate indefinitely. int[f'(x,y)]dx = f(x,y) + g(y) because the derivative of g(y) wrt x is 0. We just call it C normally because we don't need to introduce more complicated paramters than a constant most of the time. This fact occurs in some mixed differential equations.

[@user-nx6wi6eh9v]

Partial differentiation is just like normal differentiation but only according to one variable aka treating every other variable as a constant

[@manstuckinabox3679]

Ah yes, the age-old technique of invoking the mellin transform without giving my boy mellin any mellons, if mellin was still around he'd be copyright claiming left and right.

[@TheEternalVortex42]

Is the Mellin transform one of the few counterexamples of Stigler's law?

[@horserous]

Integration is difficult. Yes some nations insist on integration, courses and language basics, equally hard. Its easy for the tutor to say just differentiate it. So cheat by using Maple, and then try to figure it out. If i recall partial fractions, substitutions and bit of Heaviside was enough for me as a kid.

[@franknoir9378]

are there any videos of yours or others i can or should watch first in order to understand your videos? i already know about integrals but i dont really know about those gamma, digamma, euler mascheroni constants and the likes and really wanna understand your videos 😭😭😭

[@maths_505]

Well you could watch em in the order of upload

[@giuseppemalaguti435]

Ho provato con I(a)=x^a....I=I'(0),ma poi boh .

[@Tanvir_Ahmed_Earth]

Lol