Intro to the Gamma Function

Рет қаралды 138,607

Physics and Math Lectures

3 жыл бұрын

In this video I introduce the Gamma Function.
For more videos on this topic, visit:
• Gamma Function

Пікірлер: 67

@ianlapinski5125 3 жыл бұрын

Wonderful vid but I had a chuckle when you included (10/2)! as something that now has a meaning

@actualBIAS Жыл бұрын

You sir, are a great teacher. I understood that without even pausing. That's rare. Thank you so much

@metuphys5611 Жыл бұрын

dude i love his videos, but the guy didn't even do anything. He just motivated it and gave the definition of the gamma function

@actualBIAS Жыл бұрын

@@metuphys5611 there is nothing wrong I said.

@metuphys5611 Жыл бұрын

@@actualBIAS yeah, there was nothing wrong, i totally agree. just your selection of video to comment on was kind of off. That's all.

@actualBIAS Жыл бұрын

@@metuphys5611 If you think so...

@markokuncic199 Жыл бұрын

Great video!

@arghadeepmodak9413 3 жыл бұрын

WHAT AN EXPLANATION, THANK YOU MAN :)

@ursulifts840 3 жыл бұрын

Awesome video and channel, very helpful, thank you!

@physicsandmathlectures3289 2 жыл бұрын

Glad it was helpful!

@leif1075 Жыл бұрын

@@physicsandmathlectures3289 wait I don't think this totally.clear..why isnt z the dummy variables since I'm I'm factorial you multiply n by itself n times so it shouldbe z^z-1 Terence is no need for another variable x ..thst needlessly complicates things..see what zi mean..

@zianiera 10 ай бұрын

Very good explanation.Thank you

@daffaagung 3 жыл бұрын

Started learning this this semester, thank you sir

@physicsandmathlectures3289 2 жыл бұрын

No problem!

@raulhakim Жыл бұрын

Kelas berapa kak?

@leif1075 Жыл бұрын

@@physicsandmathlectures3289 Thanks for sharing this but it didn't really explain where e ^x comes from with respect to a factorial of a non-integer so I don't think anyone can get a full understanding just from this right??.can you elaborate on that on that we know exactly why the Gama function is defined in this way? Don't know if you already covered that sorry..

@andrewdarnall9328 Жыл бұрын

Outstanding job, your lecture couldn't have been any clearer!

@ozargaman6148 Жыл бұрын

why not have z instead of z-1? wouldn't it then be r(z)=z! instead of r(z)=(z-1)!?

@user-vo6oq1bv8x Ай бұрын

Great introduction.

@curtpiazza1688 3 ай бұрын

Interesting! 😊

@purabimondal6270 2 жыл бұрын

Please make a video on Riemann's hypothesis.....

@mesterha Жыл бұрын

Great video. It would be nice to add a proof that gamma(0)=1 which, given your other proof, would establish that gamma(n+1)=n! for the positive integers.

@koush69 7 ай бұрын

Gamma(0) is undefined we can't find Gamma(n), where n

@mesterha 7 ай бұрын

@@koush69 Looking it up on Wikipedia, you are correct that Gamma(0) can't be defined to be 1 without breaking the continuity of the Gamma function so it doesn't match the factorial function for all natural numbers. One would need to add a proof that Gamma(1)=1 to establish Gamma(n+1)=n! for the positive integers. It's also interesting to see that Gamma is defined for all complex numbers except the non-positive integers. I guess you mean Gamma(n) is undefined when n

@koush69 7 ай бұрын

I didn't understand part of your explanation where you explained gamma(n+1) on the second line of integration 6:51 someone please help me as soon as possible

@__hannibaal__ 3 жыл бұрын

I m working on it; i consider factorial as special case when f(x)=x; functional factorial is: f!(x+1)=f(x).f!(x) ; not yet finished; many thing appeared to on way.

@linfengdu7636 4 ай бұрын

A quick question: why do we shift by 1 in the definition of the Gamma function?

@drekforder2952 2 жыл бұрын

What about n!!, n!!!, ... (double, tripple,... factorial?

@sucateirodawasteland2228 4 ай бұрын

Just needed the Gama(n+1)=n! Thx

@Sam-jg5zv 3 жыл бұрын

Excellent and clear explanation

@physicsandmathlectures3289 3 жыл бұрын

Glad it was helpful!

@qutrb6790 Жыл бұрын

the 10/2 factorial is indeed very weird lol

@anilkumarsharma8901 Жыл бұрын

Any general gamma function so we found out function out of function 🤣🤣🤣🤣🤣

@geraldbronco870 11 ай бұрын

Out here trying to understand Coast Contra’s bar about square root of pi

@jimh3595 Ай бұрын

I entered the weeds when the green pen came out.

@JustNow42 Жыл бұрын

The Gamma function is the only function that has these 3 properties:For x>0: f(x+1) = x f(x) and f is log convex ( ln(f) is convex) and f(1)=1 as proven by Harald Bohr (Niels Bohr's brother) and Johannes Mollerup.

@user-nf8np3cu1z 9 ай бұрын

can someone say how he differentiate and integrate in the integral at same time ?

@bipinnitrkl0459 2 ай бұрын

Integration by parts method

@kyleworrall 9 ай бұрын

Why isn’t the gamma function just x^z instead of x^z-1?? Then Gamma(n) = n!

@blzKrg 3 жыл бұрын

Helpful.

@physicsandmathlectures3289 3 жыл бұрын

Glad to hear!

@aurelsheremetaj4183 Жыл бұрын

if I pass tomorrow in my test I will subscribe to this channel 😭wish me luck

@NetheriteMinerMicrowavegang 6 ай бұрын

Did you pass

@klmrug1916 3 ай бұрын

On thiss🗣️🎶 minuss🗣️🎶 x's🗣️🎶

@ajinaajai550 2 жыл бұрын

Why real part (z)>0

@David-zi9nr 2 жыл бұрын

Why can n! also be n(n-1)! ? Keep in mind I’ve never covered factorials in any of my math classes what a shame

@avramcs 2 жыл бұрын

Kinda late but if u think about the answer can be seen in the example at the start with 1, 2 , 3, 4 when they get plotted on the graph. If you just think about it following the rules of factorials with integers , each factorial must contain the multiples used in the factorial below it. For example 3! contains the factorial 2! Because 3! Is written as (3 • 2 • 1) and we know 2! is ( 2 • 1). Thus since we can see that 2! Is contained within 3! We can then call 3 “n” and see that the factorial function for integers can be expressed as “n • (n-1)!” since we just covered that 3! Is (3)(2)(1) or 3 • (3-1)!

@abeikukakrabaatombo-sackey4813 Жыл бұрын

Can't see anything 🥲

@yesserlabidi7831 2 жыл бұрын

You missed explanations … sadly I didn’t get what you are trying to say

@physicsandmathlectures3289 2 жыл бұрын

Sorry to hear that! I'd love to hear any suggestions or specific criticisms you have.

@tranehigh Жыл бұрын

Ten halves factorial...

@andreyvasyaev 2 жыл бұрын

Очень интересно... но где то подвох... Что мы знаем о факториалах... Для начала мы знаем что факториал следующего числа равен факториалу предыдущего числа умноженному на это самое следующее число... N!= (N-1)!×N или по другому... факториал предыдущего числа равен факториалу следующего числа деленному на это самое следующее число... N!=(N+1)!/(N+1) есть еще вид (N+1)!= N!×(N+1)... значит (N-1)!=N!/N и N=N!/(N-1)! При N=1 получаем 0!=1!/1 и 1=1!/0! При N=0 получаем (-1)!=0!/0 и 0=0!/(-1)! При N=(-1) получаем (-2)!=(-1)!/(-1) и (-1)=(-1)!/(-2)! При N=(-2) получаем (-3)!=(-2)!/(-2) и (-2)=(-2)!/(-3)! При N=(-3) получаем (-4)!=(-3)!/(-3) и (-3)=(-3)!/(-4)! При N=(-4) получаем (-5)!=(-4)!/(-4) и (-4)=(-4)!/(-5)! Видим что вычисление положительных факториалов по действию очень похоже на действие возведения в степень... только множители различные... Исходя из полученных формул отрицательный факториал берется не только от отрицательного значения но и имеет смысл обратных значений для положительных факториалов N... Во всяком случае вполне возможно N!=(N+1)!/(N+1) 0!=1!/1=1 (-1)!=0!/(0)=1/(0)= 1 неделённая единица (-2)!=(-1)!/(-1)= 1/(-1)= -1 (-3)!=(-2)!/(-2)=(-1)/(-2)= 1/2 (-4)!=(-3)!/(-3)=(1/2)/(-3)= -1/6 (-5)!=(-4)!/(-4)=(-1/6)/(-4)= 1/24 (-6)!=(-5)!/(-5)=(1/24)/(-5)= -1/120... Интересно что получаются обратные значения Гамма функциям от положительных значений когда Г(N+1)=N! Г(N+1)=N×Г(N)=N×(N-1)! Немного неожиданно... Получается что для отрицательных Г(-(N+1))=1/Г(N+1)=1/N! Но есть "проблема" со знаком... Видим что постоянно через один изменяется знак при делении "факториалов" от отрицательных значений... Предположу что нужно брать для отрицательных значений N значение по модулю (а для обобщения и для положительных значений N...) N!=(N+1)!/|N+1| (N-1)!=N!/|N| 0!=1/1=1 (-1)!=0!/0=1/0= 0 (относительный ноль) или безотносительно единица неделённая что более верно... Тогда следует (-2)!= (-1)!/|-1|=1 (-3)!=(-2)!/|-2|=1/2 (-4)!=(-3)!/|-3|=1/6 (-5)!=(-4)!/|-4|=1/24... Как видим получаем обратные величины факториалов для положительных значений N... но еще идет сдвиг на один ход относительно факториалов для положительных значений N... Смею предположить что отрицательные факториалы должны считаться по формуле N!=(N+1)!/|N|... Тогда (-1)!=0!/|-1|=1/1=1 (-2)!=(-1)!/|-2|=1/2 (-3)!=(-2)!/|-3|=1/6 (-4)!=(-3)!/|-4|=1/24 (-5)!=(-4)!/|-5|=1/120... и получается что эти значения численно равны коэффициентам для нахождения "обратного факториала"... Кстати по этой же формуле получается 0!=1!/0=1/0=1 единица неделённая что наверное будет более верно... Если уж быть совсем дерзким и исходить из того что график этих значений должен бы быть хоть немного математически красив то возможно факториалы от отрицательных значений должны бы быть и сами отрицательными... Но я пока не нахожу физического смысла отрицательным значениям факториалов... (самим факториалам от отрицательных чисел смысл проявился очень явно)... к тому же придется признать что тогда при этом 0!=1/0=0 равен относительному нулю... Но это пока мои личные фантазии... и в этом надо сначала разобраться... а перед этим хорошенько подумать... Мне все же ближе "вариант с модулями"...

@oriahmphahlele4571 7 ай бұрын

Hi sir! We can't see papa

@p.j.882 Жыл бұрын

I needed a solution for upper and lower incomplete gamma function to derive poisson and gamma distribution, this doesn't help.

@ZacharyKauffman-zb2vs Ай бұрын

(10/2)! ???

@sherifffruitfly Жыл бұрын

All of these gamma function videos are RIGHT, but damn near all of them miss the entire point. None of y'all even address let alone answer the question HOW WOULD ANYONE EVER COME UP WITH THAT. As long as the definition is random-handed-down-by-god, no actual learning has happened.

@debarjandatta2170 Жыл бұрын

That's how most math is taught especially something like calculus. When you start learning calc you just made to memorize limits and formulas and standard derivatives without any context. No one takes the effort to show an intuitive proof for math. I'm a highschool student and all the calc that I have learnt is almost entirely self taught only being supplemented by few KZfaq vids Wolfram Alpha textbooks. None of my teachers take the time to explain in an intuitive sense what fuck a derivative or an integral is and how people came up with it. It's a big pain the ass and especially in my country college entrance tests are extremely competitive so you have to cram in as many formulas as possible without learning anything beyond the elementary concept it represents. It's truly a tragedy.

@kingofdice66 Жыл бұрын

Unless God gave you the definition and said "Here it is!" without any proof of how it came to be, then you explained nothing.

@zadiczane7618 5 ай бұрын

What the hell is this comment supposed to mean?

@Harwey-lz4gp 5 ай бұрын

Tf you trying to say

@zadiczane7618 5 ай бұрын

@@Harwey-lz4gp THATS EXACTLY WHAT I SAID

@yorusaka3554 3 ай бұрын

There is no discussion, we made this up and we decided it is like this.

@hedidis3753 2 ай бұрын

It was a nice intro though

@vector8310 Жыл бұрын

You have to do something about your microphone. It's capturing the sounds of every minute saliva slosh and tongue flick inside your mouth. I had to mute it.