In this video, I showed how to obtain then gamma function by simple integration and repeated application of Leibniz's Integral Rule Buy the t-shirt here shorturl.at/HNUX1
Пікірлер: 139
@mskellyrlvАй бұрын
The best explanation of the gamma function I've seen in my 70 years.
@PrimeNewtonsАй бұрын
Thank you
@thokozanimwale210925 күн бұрын
Why can't I understand 🥲
@klasta21676 күн бұрын
@@thokozanimwale2109 watch again, maybe if its too advanced, come back to it later after understanding the base concepts required to understand it
@blackovich2 ай бұрын
Hey Prime Newtons, I must say that you have an amazing talent. I watched this video for 18 minutes without getting bored. That is rare for me.
@Tabu112112 ай бұрын
same
@Emlt2 ай бұрын
You’re the coolest maths teacher ever 😊
@Thenukasenathma2 ай бұрын
❤
@bladeofthe6623Ай бұрын
Fax
@atmonotes8 күн бұрын
yes
@uwanttono40122 ай бұрын
Have just recently started to watch your videos and your enthusiasm for maths is infectious! I just wish my high school teachers and professors of the 70s had that inspirational spark!
@user-mp6zu7ik1z2 ай бұрын
these are the only videos i can watch all the way through and never get bored
@dean5322 ай бұрын
Lol and Me revisiting Gamma functions this way at the heart of the matter! 13 years have passed and nobody teaches the derivation of CRUCIAL functions like these to engineers probably because they thought it’s irrelevant but the point here is when you do a derivation you open up new doors to possibilities and your Ebbinghaus curve would be smooth as ever (you’d remember things even better!)
@spudhead1692 ай бұрын
Instant subscribe. Wonderful, keep on "tap tap tapping".
@AlphaAnirban28 күн бұрын
"In a previous video, I was accused of performing illegal activities" Best start to a math video 😂😂
@fioscotmАй бұрын
INCREDIBLE VIDEO!!!! its insane how well you explained this... Thank you for this explanation!!!
@NjugunaBK2 ай бұрын
I met the Gamma function about three days ago in the Fermi-Dirac integrals and somehow, without searching for Math tutorials, I bumped into this. How cool?
@douglasstrother65842 ай бұрын
It's all fun & games until the Fermions show up.
@Jack_Callcott_AU2 ай бұрын
Hello Mr Newton. This is a great video And I really enjoyed it. I have never seen it done this way before, and I have an MSc in pure maths. It's so clear and simple. 📳📴✅
@PrimeNewtons2 ай бұрын
Glad you enjoyed it
@mihaipuiu62312 ай бұрын
Prime Newtons.... you are Fantastic Teacher. Congratulations!
@curtpiazza16882 ай бұрын
Wow! Great lesson! I love your chalkboard penmanship! ❤ 😊
@ricardopaula408229 күн бұрын
when you said "beautiful" in the end of the deduction that's exactly the word I was thinking, I love this channel
@Timelapse_Xpl2 ай бұрын
I love his facial expressions and cool nature.
@Aivo3822 ай бұрын
I LOVE your videos. There's so much dedication, GREAT explanations, POWERFULLY INTERESTING math ideas. Easily one of my favourite math channels, if not my favourite one. Keep doing as great as you always do 8)
@drekkerscythe47232 ай бұрын
5 mins in, and I can't help but point out that you just derived the Laplace(1) =1/s
@EvilSandwich2 ай бұрын
Oh my God I was thinking the same thing as soon as I saw the 1/t. This channel just gave us a 2 for 1 deal lol
@WhiteGandalfs2 ай бұрын
The discussion around the backward factorial development and the gamma function have been enlightening to me. Finally this stuff makes sense to me. Well: People like me, who just got an engineering level math education, get the equivalent of a lecture with this videos. Keep it going! :D And concerning the content of this juggling here: That looks like a good example for the justification of mathematicians playing around with things they have just discovered to stumble by accident upon completely new stuff that blows the mind when finalized :D When i looked through wikipedia articles after the previous video on factorials, i threw the towel when it came to the deduction of the Gamma function, but with this explanation here it is perfectly fitting in to my pre-knowledge. Thanks!
@Tejuuuop2 ай бұрын
I really enjoy your lectures, your way of explaining is very cool 🌟❤️
@sergiomensitieri2 ай бұрын
Man this is the best explanation I’ve ever seen
@keithrobinson29412 ай бұрын
Great! Looking forward to the next video in this series of videos.
@JohnBrian-zs5yp2 ай бұрын
Amazing video, I really love your enthusiasm
@marcoscirineu2 ай бұрын
Simply amazing. Congratulations!!!
@m.h.64702 ай бұрын
Thank you for addressing the issue in the last video.
@inventorbrothers7053Ай бұрын
This was the explanation i needed! Thanks!
@CM63_France2 ай бұрын
Hi, Awesome! I've been trying to find a way to derive this for a long time, and you just did it! Thanks a lot! Something else : I've been working on a way to write the factorial function as a polynomial series + a rational fraction series for a while. Say : x! = a_0 + a_1 x + a_2 x^2 + ... + b_1 / (x+1) + b_2 / (x+2) + b_3 / (x+3) + ... For now I have demonstrated that the poles (the negative integers) are single, which is quite easy. I then tried to write relationships between the coefficients by applying the formula: (x+1)! = (x+1) x! and by indentifying coefficients. But it's a bit difficult, you quickly get complicated formulas and you are kind of sailing backwards. By taking x=0 or x=1 you get some simple formulas, but that's all. Do you know a better way to do that?
@Orillians2 ай бұрын
The most exciting Prime newtons video aside from the cover up method ngllll. This IS BRILLIANT
@user-nd7rg5er5gАй бұрын
excellent work! Thank you for making this video!
@flowingafterglow6292 ай бұрын
So are you conceding that you did the "illegal" things in the last video? Because, yes, you did. I'm glad you mad this response (and it's cool you have responded so quickly)
@johnplong36442 ай бұрын
I have Totally forgotten Calculus I can’t follow this Actually. I need to Start at Trigonometry going to Pre-calculus I am at a Algebra 2 level or College Algebra level with some Trigonometry knowledge.You an a extremely intelligent person and one hell of a teacher You have a passion for it I love your attitude I am 66 I will be auditing Trigonometry at my local college this fall Then taking Calculus 1 I have a young student who I am tutoring in Pre-Algebra He wants me to to be able to help him out in Trigonometry and Pre-Calculus Actually He is Algebra 1 Ready He was totally failing math The light has been turned on And all cylinders are firing He is a freshman in High School He can pass Pre- Algebra now They are going to let him test out so he can Take Algebra 1 his sophomore year will be teaching him Algebra 2 now and all throughout the summer He wants to test out of Algebra 1 This fall He wants to take Algebra 2 and Geometry Junior year Trigonometry Senior year Pre- Calculus …Soo By the end of next year He will have the same math knowledge as I have right now So yeah I will be auditing math courses this fall …Yes never stop learning and it is never to old to learn It my case I forgot I did it once before I can certainly do it again And I can’t let him pass me up
@glgou46472 ай бұрын
"illegal" 😭😭😭 who are the police then
@diraction2 ай бұрын
Euler
@Razorcarl2 ай бұрын
Thank you sir for an amazing lesson
@h_kmack41322 ай бұрын
Absolutely awesome!!!!!!!!!!!!!!!
@spicymickfool2 ай бұрын
I really like this presentation. I suspect it lends itself to calculating the Gaussian integral without a complicated Feynman trick in the exponent. I typically derive the factorial by trying to find the Laplace transform of $t^n$, but that's not as parsimonious as this approach.
@ukasolaj11812 ай бұрын
my great respect 😀
@youknowwhatlol66282 ай бұрын
Hey! Thanks for your videos, friendo, keep up the work 😎
@user-ul3lo7mc5z29 күн бұрын
Amazing 🎉🎉
@SimchaWaldman2 ай бұрын
Why was the Gamma function defined as 𝛤(z) = (z - 1)! and not simply 𝛤(z) = z! ?
@ahmetalicetin53312 ай бұрын
We actually did that (see Π(z)) but then realized that we use (z-1)! more frequently so we just defined the gamma function as (z-1)!
@bigfgreatswordАй бұрын
The same reason why pi is 3.141... but tau is 6.283...
@SimchaWaldmanАй бұрын
@@bigfgreatsword That is why we should redefine it to be ℼ = 6.28... This way we have ℼ radians in a circle. (Oh, and for nerds/geeks we have the fomula exp(ℼi) = 1.) Bottom line: 𝜏 is just such an ugly symbol for the job!
@weo9473Ай бұрын
@@bigfgreatsword yeah why not tau = 3.1415... and pi = 6.2831...
@bigfgreatswordАй бұрын
@@weo9473 convenience
@ruaidhridoylelynch55222 ай бұрын
Great video
@ulisses_nicolau_barros2 ай бұрын
This is pure Diamond. Could you, please, bring some Integral Equations theories?
@Harrykesh6302 ай бұрын
Elegant ✨!
@johnconrardy848620 күн бұрын
love your vidieo's
@shourjyobiswas170418 күн бұрын
great explaination liked and subbed
@mistervallus1852 ай бұрын
when you assumed that the area was half when you took half the bounds, you should’ve proved, or at least mentioned in passing, that it was because the function was symmetric
@dirklutz28182 ай бұрын
x² is an even function and therfore symmetric
@mab931617 күн бұрын
Elfantastico !! ✌
@punditgi2 ай бұрын
Always count on Prime Newtons! ❤🎉😊
@superuser86362 ай бұрын
Great videos! Now I think we are ready for the LaPlace transform 😅
@dengankunghacharles1115Ай бұрын
Well done sir🎉🎉🎉🎉🎉🎉
@user-by1xn7hc9v2 ай бұрын
Prime Newton =passion for Math.
@holyshit9222 ай бұрын
This is the rule of differentiating the image applied to L(1) Yes L(t^{r}) = Γ(r+1)/s^{r+1}
@lumina_Ай бұрын
yo that was so cool!!! Thank you for this video I am actually in a state of math euphoria right now
@AlirezaNabavian-eu6fz2 ай бұрын
Excellent
@douglasstrother65842 ай бұрын
"Mammagamma" ~ The Alan Parsons Project
@conrad53422 ай бұрын
Is it just me or is anyone else listening wondering if Bob Ross just started to present math here? .. thank you for the nice video.
@haroldosantiago8192 ай бұрын
Don"t worry Master, u are a good Guy. The contraditory always be...
@Subham-Kun2 ай бұрын
7:19 Sir could you kindly do a video proving the "Leibniz Integral Rule" ?
@joeystenbeck66972 ай бұрын
I have a related question. Is the intuition behind it just that partial derivative with respect to t and the integral of x are constant relative to each other? I'm not sure if the proof goes deeper or if the proof's complexity is largely rigor. Full disclosure I haven't looked into it much yet
@Cookie8277227 күн бұрын
Very cool video but how does the Gaussian integral fit in to this? Doesn't changing x2 to tx change the nature of it, especially given that t isn't a function of x?
@hammadsirhindi13202 ай бұрын
Is there any method to calculate the approximate value of gamma(1/3)?
@majora42 ай бұрын
I have a question regarding the step taken at 1:39. I can clearly see it works here, but does it *always* work? In other words if given some f(x): R -> R and real number L such that Int{-inf to inf} f(x) dx = L, is it always true that Int{0 to inf} f(x) dx = L/2?
@ingiford1752 ай бұрын
It works because f(x) is an even function. If f(x) is an odd function then the original integral is 0 for any R, but the {0 to inf} can be anything
@majora42 ай бұрын
@@ingiford175 Ah, yeah, that makes a lot of sense. It hadn't occurred to me until you said so that e^(x^2) is an even function because, for whatever reason, it doesn't really "feel" even to me.
@user-rq6gd8yy2t2 ай бұрын
Great video as always, but I'm confused why we put t=1 like are we allowed to assume this or just to make things easier , and if so why not other number like 2,3,4 etc... . And again thank you so much for thus great channel ❤
@joeystenbeck66972 ай бұрын
Iiuc the integral with t in it is more general than the gamma function. In other words, the gamma function is a specific instance of it. Prime Newtons showed us how to prove that the more general integral was equal to factorial over t^Z, and then showed that replacing t with 1 gives us the gamma function.
@Targeted_1ndividualАй бұрын
The idea is that this is a general explicit definition of the gamma function, which works for all real t. Setting t = 1 just makes for a simpler expression.
@kikilolo677124 күн бұрын
4:57 There you assume that t>0 but what if t
@alexiopatata40482 ай бұрын
Is it possible to calculate the integral of the gamma function?
@tomvitale35552 ай бұрын
Phew! Truly a thing of beauty! But how do you think that the discoverer of the Gamma function started the derivation with the integral (from 0 to infinity) of e^(-tx) dx? Do you think that he/she already knew the "destination" and reverse-engineered to get there? For example, noticed that if you keep differentiating e^(-x) dx you'd get the form of a factorial as the multiplier?
@ingiford1752 ай бұрын
I think it the concept 'modern' concept of the gamma function first came up with writings between Euler and Goldbach
@tomvitale35552 ай бұрын
@@ingiford175 Whoever did it, was brilliant!
@wolphyxx2 ай бұрын
New video droped 🔥
@naturallyinterested75692 ай бұрын
I still don't know why one does this shift from n to z. It looks like just an obfuscation. Does it bring any benefits?
@PrimeNewtons2 ай бұрын
n is generally perceived to be natural numbers. The gamma function takes a lot more than that.
@naturallyinterested75692 ай бұрын
@@PrimeNewtons Sorry, I don't mean the exchange of symbols, I mean the input shift by one.
@flowingafterglow6292 ай бұрын
@@naturallyinterested7569 Yeah, I agree. Because if you look at the last expression, you could just come back and resubstitute n = z -1 and it's just a simple expression for n! There must be something else here.
@PrimeNewtons2 ай бұрын
Oh. That's the only way you can enter the input directly as the argument of the function. Otherwise, you'd be writing Gamma(x-1) or Gamma (x+1) and not Gamma(x)
@naturallyinterested75692 ай бұрын
@@PrimeNewtons But that's exactly what I mean, without this shift in the definition of Gamma(x), for which I know no reason, we would have Gamma(n) = n! What I don't know is for what reason (other than to annoy me ;) is that shift there?
@himadrikhanra74632 ай бұрын
Gama 1/2= root pi...polar coordinate?
@KarthikeyanARA9 күн бұрын
Can you end the video by showing the whole board, so i can take notes,......(Keep doing, you doing great)
@PrimeNewtons9 күн бұрын
I'll practice doing that. Thanks for the suggestion.
@TheLokomente2 ай бұрын
💯
@elegantblue452 ай бұрын
Doesn't the limit depend of the sign of t? Because if t is negative then lim_{R \to +\infty} e^(-tR) = + \infty
@micharijdes98672 ай бұрын
It does. t > 0 had to be specified
@elegantblue452 ай бұрын
@@micharijdes9867 Yeah! But youtube teachers tend to not be as rigorous
@samueldada4803 күн бұрын
please i need same explanation on beta function
@treybell405012 ай бұрын
Law abiding citizen newton yessir
@mathpro9262 ай бұрын
I enjoy with your class thank you teacher
@gustavozola71672 ай бұрын
Excellent video! But can you explain why you are allowed to simply say that “t=1”?
@plucas20032 ай бұрын
t é um valor arbitrário, então, pra facilitar os cálculos, ele fez t=1
@DEYGAMEDU2 ай бұрын
sir please show how e is created
@johnka54072 ай бұрын
Why does e^(1/Rt) become 0
@micharijdes98672 ай бұрын
It is because it says 1/(e^Rt), not e^(1/Rt) as I thought it did at first. In this case of course, e^Rt is very big and 1/e^Rt goes to 0
@turkishkebab312 ай бұрын
hello sir can you solve lim n -> inf (1/n^2) * Sum[Sum[b^2-d^2,{d,3n,10cn}],{b,2n,5an}]
@camiloonatecorrea71902 ай бұрын
I love you kanye
@donwald343629 күн бұрын
Illegal factorial confession lol!
@senuradilshan80952 ай бұрын
Hello sir
@syedmdabid71912 ай бұрын
The factorial of a negative number is UNDEFINED or INFINITY. So, gamma of ZERO is infinity. And So the logarithmic value of negative number is imaginary.
@PrimeNewtons2 ай бұрын
No. Factorial of a negative INTEGER is undefined
@sebas31415Ай бұрын
Wdym 0!=1
@DeluxeWarPlaya2 ай бұрын
Use b
@siroofficialfan6584Ай бұрын
Cam on vi da den
@bigfgreatswordАй бұрын
💀🙋🏿♂️
@ProactiveYellow2 ай бұрын
Wait, 0! Isn't supposed to work? The number of arrangements of a size 0 ordered set? You have only one possibility: take none (which is taking all), thus 0!=1
@mikefochtman71642 ай бұрын
I think that's sort of the point of the video. If you define factorial simply in terms of set theory (permutation of n distinct objects) then size 0 set doesn't make sense. But it's observed that the repeated differentiation of that integral can ALSO be a definition of 'factorial'. And in that context, we have a different way to calculate n!. Using this new method definition, it DOES have a value for 0! and 'can be shown....' to have a value of 1.
@mikefochtman71642 ай бұрын
In math, sometimes things have different meanings depending on context. Like 'parallel lines' in flat plane geometry never meet. But in non-Euclidian, 'parallel lines' can mean something different and in that context they can. Maths.... what can I say?
@ProactiveYellow2 ай бұрын
@@mikefochtman7164 except that a set of size zero makes perfect sense, it is the empty set, which has precisely one permutation, so my confusion is why some would claim that 0! is undefined in the classic sense
@flowingafterglow6292 ай бұрын
@@ProactiveYellow But he didn't base his derivation on the interpretation that it is the number of permutations. He used the function n! = n(n-1)(n-2)...3*2*1 and then tried to slip in a 0 for the last term. As was pointed out in the last video, you can't do that because the factors in the function necessarily terminate at 1. If he would have used set theory, it would have been a different argument.
@allozovsky2 ай бұрын
@flowingafterglow629 But then it would be an _empty product,_ that is a product of an empty list of factors, which by convention is equal to the neutral element of multiplication, that is 1. In the same manner, like an _empty sum_ is equal to the neutral element of addition, that is 0. So it makes perfect sense.
@surendrakverma5552 ай бұрын
Good
@GFlCh2 ай бұрын
Why do I understand things when you explain it but otherwise, not so much?
@PrimeNewtons2 ай бұрын
Because you're a good learner.
@zyntolaz2 ай бұрын
Nice work, except that you cannot have t = 0, and you never point out this limitation. More sleight of math? 🙂
@SamuelDonald-pr2uu2 ай бұрын
Nice job ❤
@DeluxeWarPlaya2 ай бұрын
Don't use R
@PrimeNewtons2 ай бұрын
Now that I think about it, I should not have used R. Maybe r.