The Weierstrass Definition of the GAMMA FUNCTION! - Proving Equivalence!

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  • Опубликовано: 5 сен 2024
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    Gamma derive: • DERIVING THE GAMMA FUN...
    Euler Def: • ONE NEAT PROOF! Derivi...
    Gamma Const: • The Euler-Mascheroni C...
    Today we are going to backwards engineer the WEIERSTRASS Definition of the gamma function to our already derived Euler-Gauss Definition! Infinite Product fun! =D Enjoy :)
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Комментарии • 56

  • @vangrails
    @vangrails 5 лет назад +44

    The gamma function is the gift that keeps on giving.

  • @everlastingauraX
    @everlastingauraX 5 лет назад +70

    The gender of this operator is left as an exercise to the reader.

    • @ianweckhorst3200
      @ianweckhorst3200 8 месяцев назад

      Please define gender in terms of algebra, I missed the class on gender

  • @vijayank1170
    @vijayank1170 5 лет назад +29

    Surely you are joking Mr Feynman

  • @neilgerace355
    @neilgerace355 5 лет назад +5

    9:20 yeah I got confused last time you did this, but it makes sense to me now because you are taking the limit

  • @mihaipuiu6231
    @mihaipuiu6231 2 месяца назад +1

    Flammable...you are a very good teacher. Your explanation is perfect, very clean, and nice.Thanks

  • @neilgerace355
    @neilgerace355 5 лет назад +15

    0:55 Ah, good. I've been waiting to learn about Weierstrass from someone who can pronounce it

  • @duncanw9901
    @duncanw9901 5 лет назад +9

    I'd say that the pi is an infinity grill. Because it looks like a literal grill.

  • @rahmatkhan3982
    @rahmatkhan3982 3 года назад +4

    well explained....

    • @PapaFlammy69
      @PapaFlammy69  3 года назад

      thx! :)

    • @rahmatkhan3982
      @rahmatkhan3982 3 года назад

      @@PapaFlammy69 can recommend me a book related to Gamma function and its analytic continuation ,because i m working on my M.phil thesis and the topic is Multiple zeta functions ,

  • @kalvin90210
    @kalvin90210 5 лет назад +5

    Oh my God! BRAVO 🍄 and I absolutely cannot control myself for the long-awaited digamma and polygamma functions!!!! 🍄🍄🍄

  • @J.P.Nery.N.
    @J.P.Nery.N. 5 лет назад +4

    My mother language is portuguese and here the product is called "o produto", with "o" indicating it's male. So it's an infinity boiiiiiiiiiii hell yeah! Lol

  • @ralphhebgen7067
    @ralphhebgen7067 5 месяцев назад +2

    Ok I am going to say it. Sometimes you are supremely funny. “This is some stuff you can use to get rid of your spare time” 😂😂😂. “We can do the limit Hadoken”. That one must be the coolest way to refer to limit operations EVER. 😂😂😅

    • @PapaFlammy69
      @PapaFlammy69  5 месяцев назад

    • @skyethebi
      @skyethebi 4 месяца назад

      I really hope he refers to it as a limit Hadoken when he teaches it to his students

  • @wraithreaper9416
    @wraithreaper9416 4 года назад +3

    If you define your product in order to express n as being of the form k/k-1 then your index k has to be equals to or greater than 2, running up until n because setting k=1, as you proposed, means dividing by zero. Also, if terms on the product will be of the form (k+1)/k. index may run from 1 to n-1. Please correct me if I'm wrong, Papa Flammy.

  • @The1RandomFool
    @The1RandomFool 4 года назад +2

    Infinite sum is infinity boi, infinite product is infinity grill.

  • @ylenolsreppeptgs
    @ylenolsreppeptgs 5 лет назад +3

    i cant wait for some of the sexy definite integrals papa is about to solve after he derives the taylor expansion for ln(gamma(1 + x))

  • @RobsMiscellania
    @RobsMiscellania 5 лет назад +6

    Goodbye free time

  • @leafbaguette
    @leafbaguette 5 лет назад

    this formula is so nice, it makes the poles at the negative integers explicit

  • @Azelide
    @Azelide 5 лет назад +3

    Product notation = letter Pi = Cutie Pie = female 🤣

    • @peterbrough2461
      @peterbrough2461 5 лет назад +2

      It's got that lemniscate above the π to suggest it's "decorated with ribbons" so I'd go with female too (if I had to make a choice) 👽.

  • @duncanw9901
    @duncanw9901 5 лет назад +7

    Them: what u watch
    me: polygamma function boiiiiiiii

  • @silentinferno2382
    @silentinferno2382 5 лет назад +3

    Where can I find that book in the intro??? I'm in desperate need of it!!!11!!!!!1!

  • @winters_4611
    @winters_4611 5 лет назад +12

    Do you use hagoromo chalk?

    • @everlastingauraX
      @everlastingauraX 5 лет назад +4

      @@PapaFlammy69 ruclips.net/video/PhNUjg9X4g8/видео.html Its a video that gets spammed on Ads. Only the cool math bois use it according to the telly.

  • @borisivanov9665
    @borisivanov9665 5 лет назад +2

    Product is big and boxy, so it’s a boi. Sum has a somewhat hourglass shape, so it’s the sum that must be a grill.

  • @bogdancorobean9270
    @bogdancorobean9270 5 лет назад +3

    Ma boi Weierstrass

  • @frozenmoon998
    @frozenmoon998 5 лет назад +8

    Identifying the gender of the mathematical notation would be the same as considering things about mathematicians. For example, that infinity boys, such as yourself, papa, would have to be something different than what they are - geniuses.

    • @frozenmoon998
      @frozenmoon998 5 лет назад

      @@PapaFlammy69 I do believe however, for the sole purpose of being brave and all, that the gender of the notation is pure engineer :)

    • @youurdream182
      @youurdream182 5 лет назад +2

      @@frozenmoon998 I would say that it's gender is an apache helicopter, but its only a speculation.

    • @hey4067
      @hey4067 5 лет назад

      Numbers have an end : scientific truth.
      - Mohamed 🆎🅰️👻 -

  • @MathematicsOptimization
    @MathematicsOptimization 5 лет назад +1

    But what *is* a bröh-moment?!
    -> when the autofocus is still not disabled

  • @marcorademan8433
    @marcorademan8433 5 лет назад +3

    Infinity gurl since the legs are open

  • @mrandersonpw53
    @mrandersonpw53 5 лет назад

    2 min 35 seg of introduction? Man, you are getting harder in every next video. So Savage Papa.

  • @49fa75
    @49fa75 5 лет назад +1

    This is epic.

  • @neilgerace355
    @neilgerace355 5 лет назад +1

    1:30 Maskeroni ... But Germans haven't listened to Italians properly since about 1933 ... :)

  • @ziacbe100
    @ziacbe100 2 года назад

    what is your hodoku at 4:28, is that a Japanese anime thing?

  • @alphahelix5526
    @alphahelix5526 5 лет назад

    4:20 kaaa-me-haaa-me-ha !☄️

  • @tanvec
    @tanvec 5 лет назад +1

    I'm going to use mathhematical hadouken to wake my students up

  • @8vabc338
    @8vabc338 5 лет назад +7

    I know that in Germany now is the age of a great tolerance. Some people may be offended if you ask them about their gender.

    • @8vabc338
      @8vabc338 5 лет назад +5

      But you can ask me for sure. My answer is: a camel.

    • @bogdancorobean9270
      @bogdancorobean9270 5 лет назад

      There are more than two genders

    • @8vabc338
      @8vabc338 5 лет назад +1

      @@bogdancorobean9270 there is a gender of confused people, plus men and women. Watch the video "why are you gay?" On youtube, it is the best video about it. Very funny, but true.

    • @8vabc338
      @8vabc338 5 лет назад +1

      I am talking about this video ""Why Are You Gay?" - LGBT Homosexuality Debate - Is It Natural? (FULL INTERVIEW)"

    • @angelmendez-rivera351
      @angelmendez-rivera351 5 лет назад

      8v ABC any video suggesting it is unnatural is scientifically innaccurate

  • @animalfarm7467
    @animalfarm7467 5 лет назад

    Jetzt ist dieses Video viel interessanter als das Zählen in binär.

  • @jorgesponja3042
    @jorgesponja3042 5 лет назад

    If you multiply z in both size you will get z(gamma(z)) and since gamma(z) is (z-1)! now we will get gamma(z+1), or as bprp like to say: pi(z)
    Or am I wrong?

  • @goatmatata2798
    @goatmatata2798 5 лет назад

    I have a humble request,,,, please create a video where u prove gauss's multiplication theorem for the gamma function, I have tried it a million times but just can't get it right,, please papa😭😭😭😭😭😭😭😭😭😭😭

  • @MrAssassins117
    @MrAssassins117 5 лет назад

    Digamma and polygamma sounds like wonder girls , so this is like an hybrid hermafrodite boi

  • @kuravasic
    @kuravasic 5 лет назад

    Can't wait to see polygamma functions!

  • @komalrajesh7429
    @komalrajesh7429 5 лет назад

    Sir hindi me explain kariye