You’re the coolest maths teacher ever 😊

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.

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!

these are the only videos i can watch all the way through and never get bored

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. 📳📴✅

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!)

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)

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)

Wow! Great lesson! I love your chalkboard penmanship! ❤ 😊

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?

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!

Prime Newtons.... you are Fantastic Teacher. Congratulations!

5 mins in, and I can't help but point out that you just derived the Laplace(1) =1/s

Simply amazing. Congratulations!!!

I really enjoy your lectures, your way of explaining is very cool 🌟❤️

Great! Looking forward to the next video in this series of videos.

The most exciting Prime newtons video aside from the cover up method ngllll. This IS BRILLIANT

Amazing video, I really love your enthusiasm

Why was the Gamma function defined as 𝛤(z) = (z - 1)! and not simply 𝛤(z) = z! ?

Thank you for addressing the issue in the last video.

excellent work! Thank you for making this video!

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?

Instant subscribe. Wonderful, keep on "tap tap tapping".

I love his facial expressions and cool nature.

Man this is the best explanation I’ve ever seen

This is pure Diamond. Could you, please, bring some Integral Equations theories?

Thank you sir for an amazing lesson

Hey! Thanks for your videos, friendo, keep up the work 😎

Great videos! Now I think we are ready for the LaPlace transform 😅

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.

Absolutely awesome!!!!!!!!!!!!!!!

Always count on Prime Newtons! ❤🎉😊

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 ❤

Elegant ✨!

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

Great video

my great respect 😀

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

7:19 Sir could you kindly do a video proving the "Leibniz Integral Rule" ?

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.

Excellent

"Mammagamma" ~ The Alan Parsons Project

This is the rule of differentiating the image applied to L(1) Yes L(t^{r}) = Γ(r+1)/s^{r+1}

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?

Don"t worry Master, u are a good Guy. The contraditory always be...

💯

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?

Doesn't the limit depend of the sign of t? Because if t is negative then lim_{R \to +\infty} e^(-tR) = + \infty

Is it possible to calculate the integral of the gamma function?

Is there any method to calculate the approximate value of gamma(1/3)?

New video droped 🔥

Prime Newton =passion for Math.

Gama 1/2= root pi...polar coordinate?

I enjoy with your class thank you teacher

Excellent video! But can you explain why you are allowed to simply say that “t=1”?

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?

Law abiding citizen newton yessir

"illegal" 😭😭😭 who are the police then

hello sir can you solve lim n -> inf (1/n^2) * Sum[Sum[b^2-d^2,{d,3n,10cn}],{b,2n,5an}]

I love you kanye

Why does e^(1/Rt) become 0

sir please show how e is created

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.

Good

Hello sir

Use b

Nice work, except that you cannot have t = 0, and you never point out this limitation. More sleight of math? 🙂

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

Why do I understand things when you explain it but otherwise, not so much?

hey man pls let my family go

Don't use R

Nice job ❤