A cool iterated integral

Поделиться
HTML-код
  • Опубликовано: 20 окт 2024

Комментарии • 32

  • @mcalkis5771
    @mcalkis5771 3 дня назад +8

    I was about to comment that thid is probably the most straightforward integral you've solved, but then dilogarithms appeared.

    • @sergiokorochinsky49
      @sergiokorochinsky49 День назад

      Yes... dilogarythm appeared, and leaving the original integral as a "fancy constant" plus another integral is the same as not-solving the original integral. I'm disappointed.

  • @jaimequerol27182
    @jaimequerol27182 3 дня назад +13

    Video about Aery's differential equation when?

    • @maths_505
      @maths_505  3 дня назад +6

      OHHHH I FORGOT ABOUT THAT ONE!
      Thanks for the reminder homie

    • @xinpingdonohoe3978
      @xinpingdonohoe3978 3 дня назад

      Will it also cover the incomplete Airy functions/Scorer's functions Gi(x) and Hi(x), or just the complete Airy functions Ai(x) and Bi(x)? I know Gi(x)+Hi(x)=Bi(x), but they're still kind of significant.

    • @zlodevil426
      @zlodevil426 3 дня назад

      @@maths_505I love your honesty lol

  • @orionspur
    @orionspur 3 дня назад +12

    0:05 Threesome = Triple integral with exactly one log. 🤔✅

  • @CM63_France
    @CM63_France 2 дня назад

    Hi,
    1:53 : maybe we know by heart that the antiderivative of ln x is x ln x - x 🙂
    "terribly sorry about that" : 1:03 , 1:57 , 3:36 , 4:32 , 4:40 , 6:53 , 7:33 , 10:19 ,
    "ok, cool" : 1:09 , 2:17 , 3:40 , 5:09 , 10:26 .

  • @eu7059
    @eu7059 3 дня назад +3

    You should add a +1ln1 to the result to complete the stair, and if you’re really felling fancy today, you can even add -0ln0 and “define” it as its limit when x goes to 0

    • @maths_505
      @maths_505  3 дня назад

      OHHHHH DAMN I AM SO MAD RN FOR NOT THINKING ABOUT THAT😭

  • @MrWael1970
    @MrWael1970 2 дня назад

    Very nice integral. Thank you

  • @pranavaggarwal7965
    @pranavaggarwal7965 3 дня назад +6

    I am the first one to look out this cool integral with my eyes😢

  • @SuperSilver316
    @SuperSilver316 3 дня назад +1

    Good practice with these is to use the inversion formula of the Dilogarithm to write Li_2(-2) in terms of Li_2(-1/2) and other terms, but this is also fine!

  • @gesucristo0
    @gesucristo0 3 дня назад +3

    How to deal with the fact that the di-logarithm converges for z in the unit circle and -2 clearly doesn’t belong in there?

    • @gesucristo0
      @gesucristo0 3 дня назад

      @@uvtears but 2^2=4>1, so…

    • @SuperSilver316
      @SuperSilver316 3 дня назад +2

      You can use an inversion formula for the dilogarithm
      Li_2(-2) = -Li_2(-1/2)-pi^2/6-ln^2(2)/2

    • @vascomanteigas9433
      @vascomanteigas9433 3 дня назад

      Analytical continuation goes brrrr... 😂
      Using the integral form of dilog are easy to do this step.

    • @maths_505
      @maths_505  3 дня назад

      @vascomanteigas9433 indeed

  • @acpwnd2020
    @acpwnd2020 2 дня назад

    Bro, you’re so clever. How do you find/discover these problems? Is there a resource I can use to practice problems as challenging as these?

    • @maths_505
      @maths_505  2 дня назад

      @@acpwnd2020 this is from the Romanian mathematical magazine. Problem by Ankush Kumar parcha

  • @fengshengqin6993
    @fengshengqin6993 2 дня назад

    Not very satisfied with Li2(-2) ,what is it exactly ?

  • @giuseppemalaguti435
    @giuseppemalaguti435 2 дня назад

    ln(27/4)-3+INT(ln(2+z)/(1+z)..z=0...1)

  • @sebastianlopezgiraldo21
    @sebastianlopezgiraldo21 2 дня назад

    Hey bro do you have any book? I'd like to know if you have written a math book

  • @monishrules6580
    @monishrules6580 3 дня назад

    Solve schrodinger equation

  • @n8cantor
    @n8cantor 3 дня назад

    [Rammstein voice]
    X
    XY
    XYZ

  • @alvercury
    @alvercury 2 дня назад

    You should be terribly sorry about being terribly sorry for like a gazillion times in a single video

    • @maths_505
      @maths_505  2 дня назад +1

      Ah yes ofcourse terribly sorry about that