How Ramanujan would DESTROY this tough integral

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  • Опубліковано 6 лют 2025
  • A fascinating integral solved using Feynman's trick and ramanujan's master theorem.
    Proof of the master theorem:
    • How Ramanujan proved h...
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КОМЕНТАРІ • 57

  • @Player_is_I
    @Player_is_I 5 місяців тому +59

    Bro tried to sneak in Feynman

  • @cleojosei
    @cleojosei 5 місяців тому +28

    I never get tired of the Feynman technique, so cool!

    • @maths_505
      @maths_505  5 місяців тому +5

      @@cleojosei well I've got a whole playlist so....

    • @acelm8437
      @acelm8437 5 місяців тому +5

      More like reverse Feynman, since we're differentiating the simpler integral instead of integrating

    • @parthasur6018
      @parthasur6018 5 місяців тому

      The "Feynman Technique" is known in calculus as "differentiation under the integral sign" and was well known long before Feynman was born!

  • @leroyzack265
    @leroyzack265 5 місяців тому +8

    It was an absolute beast and the Euler Mascheroni constant did not disappear and the master theorem was of good help.

  • @mcalkis5771
    @mcalkis5771 5 місяців тому +3

    That proof of convergence in the beginning is much appreciated.

  • @stefanalecu9532
    @stefanalecu9532 5 місяців тому +8

    You plugged your merch like a champ 🏆

  • @Samir-zb3xk
    @Samir-zb3xk 5 місяців тому +6

    I solved it by placing the parameter in the argument of the sine function:
    I(a) = (0 to ∞) ∫ sin(ax²) ln(x) / x² dx
    I'(a) = (0 to ∞) ∫ cos(ax²) ln(x) dx
    I'(a) = Re (0 to ∞) ∫ e^(-iax²) ln(x) dx
    Which (after substitution) can by solved via the derivative of the gamma function using Γ'(1/2) = -√π (γ+ln(4))
    And then after taking the real part, integrating to recover I(1) is fairly straightfoward

    • @Flylearjet9
      @Flylearjet9 5 місяців тому

      That’s what I did as well. Doing gamma function later is better

    • @Flylearjet9
      @Flylearjet9 5 місяців тому

      It’s not negative btw it’s positive e^(iax²)

    • @Samir-zb3xk
      @Samir-zb3xk 5 місяців тому

      @@Flylearjet9 cosine is an even function so the real part of e^(ix) and real part of e^(-ix) is both cos(x)

    • @Flylearjet9
      @Flylearjet9 5 місяців тому

      @@Samir-zb3xk oh crap I forgot, I used RMT, but for this technique we take the derivative of the gamma function of 1/2. Then what do we do. I have one solution, it I want to know the other solution. RMT is what I used though

    • @Flylearjet9
      @Flylearjet9 5 місяців тому

      @@Samir-zb3xk also do you. Have insta, I can send you to RMT that I did

  • @GiornoYoshikage
    @GiornoYoshikage 5 місяців тому +5

    I guess one of solutions is substitution and Feynman's trick applied to the integral computed via Laplace transform (haven't watched the video yet)

  • @jakehobrath7721
    @jakehobrath7721 4 місяці тому +2

    Love your videos but every version of any letter you write is some form of a rotated or reflected letter P

  • @maxvangulik1988
    @maxvangulik1988 5 місяців тому +6

    11:49 "similarly" ahh cut

  • @الْمَذْهَبُالْحَنْبَلِيُّ-ت9ذ

    The function isn't bounded on the interval (0,1); at least not for negative values of α. In fact the integral only ever converges on that interval if α > -3.

  • @barryzeeberg3672
    @barryzeeberg3672 4 місяці тому

    9:45 pi/8 is how you would slice up a large pizza

  • @marcelobrenha
    @marcelobrenha 5 місяців тому

    hey Kamal, i have been following your videos for some 3 months or so and I think (know) that you are a fu%^$# genious. I want you to have as much success in the networks as you can get and for that reason I would suggest once in a while to go down on the difficulty level of the integral or any type of problem your are dealing with to talk to a much wider range of people. Of course what makes you fenomenal and this is what many of your current followers are after is that you are a fuck**ing genious that can solve unbelieveble problems like it is nothing, but just here and there, try to solve something that normal people would like to try and solve. I am pretty sure you will have a much broader audince by just piking some easier problems and solving them online once in a while. Cheers and keep going. Your are a monster

    • @maths_505
      @maths_505  5 місяців тому +1

      I'm not a genius but yeah I've been thinking of diversifying content for a while.

  • @BikeArea
    @BikeArea 5 місяців тому

    This must be one of the most hilarious product placements I've ever stumbled upon thus easy to forgive. 😊

  • @alielhajj7769
    @alielhajj7769 5 місяців тому

    The integrand is not bounded between 0 and 1, it is bounded for values of alpha greater than pr equal to -2 however this is not enough for differentiation, you need boundedness pr convergence on an open interval containing the value -2, fortunately we have convergence for value of alpha strictly greater than -3 (using some p value test), combining with the convergence of the tail for alpha strictly less than -1 we have garanteed convergence for alpha on the interval (-3,-1) which indeed contains -2 and hence we can differentiate under the integral at -2, the lower bound of -3 is strict however the upper limit can be pushed further and need some more advanced convergence test

  • @MrWael1970
    @MrWael1970 5 місяців тому

    Very cool. Thank you.

  • @anas-altaleb
    @anas-altaleb 5 місяців тому

    Why its ends with divergence when we use laplac tran

  • @ericthegreat7805
    @ericthegreat7805 5 місяців тому

    Can you make a video on the pattern for integrals of the form
    Sin(x^n)/x^n
    Since I assume they are recursively related to
    Sin(x)/x

  • @CM63_France
    @CM63_France 5 місяців тому +3

    Hi,
    "ok, cool" : 0:58 , 8:04 ,
    "terribly sorry about that" : 7:56 , 9:55 .

  • @yoav613
    @yoav613 5 місяців тому

    Nice!! 8 monthes ago you said that you are going to make a video about Hardy's proof to RMT,so should we wait 8 monthes or more?😂💯

  • @TheIndianPrince_
    @TheIndianPrince_ 5 місяців тому +1

    Destroying Integrals 😤😤

  • @empanador2748
    @empanador2748 5 місяців тому +9

    No views in 20 seconds? Bro fell off (love the vids)

  • @dharunpranay8581
    @dharunpranay8581 5 місяців тому +3

    A nice promotion of your products of Gamma Function

  • @michakupczyk9560
    @michakupczyk9560 5 місяців тому +1

    Response to title :
    By taking a nap

    • @maths_505
      @maths_505  5 місяців тому

      @@michakupczyk9560 😂😂😂

  • @chancia8990
    @chancia8990 5 місяців тому

    utter sick

  • @kingzenoiii
    @kingzenoiii 5 місяців тому +1

    LEIBNIZ REPRESENT!!

  • @الْمَذْهَبُالْحَنْبَلِيُّ-ت9ذ

    Brilliant marketing techniques however I have to say!

  • @Khushal435
    @Khushal435 5 місяців тому +1

    First of all Ramanujans master theorem is very difficult to prove...

  • @zemm9003
    @zemm9003 5 місяців тому

    This is Feynman's trick.

  • @modern_genghis_khan0393
    @modern_genghis_khan0393 5 місяців тому

    Isn't it Feynman technique ?

    • @maths_505
      @maths_505  5 місяців тому +1

      More of a Collab between the two. I have more dedicated videos that I attribute to Feynman's trick.

  • @wolfcanyon
    @wolfcanyon 5 місяців тому

    Thumbnail is cursed

  • @Pratyush641
    @Pratyush641 5 місяців тому

    First

  • @borhenbouchniba
    @borhenbouchniba 5 місяців тому

    Hello @Maths 505 I need a help to solve an equation how can I contact you please

  • @diogeneslaertius3365
    @diogeneslaertius3365 5 місяців тому +1

    Probably the same way he destroyed his underage wife.