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This isn't zetamath, but it is good!

Wounderful ! Sir. Love and respect from India. ❤🙏

Thx

great video !

More beautiful more concrete

Wicked cool!!

I'm surprise that you break down gamma function and proof it precisely, any way, thank you sir

You can also derive it in a nice way by looking at the Poisson distribution and setting that equal to its binomial representation as n goes to infinity and p goes to zero and write it in the form of the mean rate lambda (=np). You integrate it from zero to infinity with respect to lambda and you get 1 (quite amazingly). Just multiply by k! (The denominator of the Poisson distribution) and get the gamma function. You also can derive the gamma and beta distribution as a consequence.

This is an amazing video. I can’t believe I didn’t know this until today!

sorry if im mistaken but when taking the derivative of logx would it not be 1/[(ln10)(x)]? where im from logx generally means that the base is 10 and ln is usually used when base is e which gives 1/x as a derivative. correct me if im wrong, maybe its just difference in mathematical language haha, either way i get what the video is trying to say i just want to double confirm

that was a brilliant proof, we can do this using geometric series as well

Do you have the same video for the beta function?

why did we only consider the limit to 0?

2nd comment: So, just like that, Euler found a function that can find the factorial of real numbers? I'm still fabbergasted 😲😲

Holy Molly! THANK YOU, one of the most satisfying experiences I've had with TH-cam math videos, THIS is the kind of logical deduction that I always look for and rarely find. This proof is magnificent, elegant, crystal clear and so relieving. Thank you! You've got yourself a new subscriber.

Bonjour …intervertir la somme et la dérivée sans justification ou encore dans l une des dernières étapes où on doit imposer que le module de x doit être strictement inférieur à 1…?

Un grand 👏 bravo tout simplement

The best presentation about Gamma Function

Why isn't Euler as a popular figure as Einstein is?

Just wasted 20 minutes watching this guy do integration by parts 🙄

Thank you bro I was searching for this video a long time ago ❤❤

You cant use l hopitals rule here since it requires that we know the derivative of sine the value of which uses this identity in its proof. We are using circular logic where something proves itself.

Hi @Mathority1729 This explanation of yours is simply miraculous, neat, and suitable for beginners on Euler's proof. Moreover , it reflects the beauty of mathematician in their attempt to proof their work adequately.

This is the best approach to understand Gamma function. Thank You for this video.

1:23 Correction!!! If u=log(x)=>ln(x)/ln(10) du=1/(xln(10)) not 1/x Also d/dx(ln(x)=1/x{x>0}

Lovely! ❤

Easy to prove it works but hard to derive

I actually followed that BUT I have no idea what the gamma function is or is used for even though I could now derive it :)

Great🫡

It is absolutely unnecessary to use vulgar language in an educational channel. That might bring some extra idiots, but I’m not sure they’ll stay to the end. I personally won’t come back. Adios

Beautiful... but i do not like the 1644 connection with whatever .. it sounds like astrology stuff. No need.

Mate you "proved" k=0 at one point. This isn't rigorous.

whew I was freaking out from 16:02 to about 18:02 when I didn't see any definite integral, and was expecting you to write out the whole series lol. I'm glad you caught it after a few min.

Dude you are just phenomenal

Thankyou !!!

Finally! Thank you so much! I tried to understand Basel problem for a while and your video finally gave me everything I wanted to know. You made me smarter.

Why don't people use ln for log base e? log with the base omitted is log base 10.

It is so cool that you can write the multiplication of a sequence of integers (factorial) as a sum (integral). Such a nice video! Thanks! I used gamma function in Statistics quite a lot when proving a lot of stuff in my undergrad. I was not aware where it came from. From your explanation, now it is easy to see.

Very good! "I'll be back!"

Nice one,thanks

The first half of the video proving the Euler product formula for sine is just a basic overview for why the formula is consistent, but not a rigorous proof that it is equivalent to sin(x). The proof is much more advanced and involves integrals, and was only proven over 200 years after Euler proposed it

At 7:34 amongst all the sines and pi stuff, you introduced a tangent. Excellent!

Great video dude

And so on and so forth...

I for the first time saw your channel It was wonderful and very clear explanation. Please keep on making videos.. Thanks for your efforts🙏🙏🙏🙏

I’m sorry, but this did *not* have to be 20 minutes long. Needlessly dragging this over

Wow, that was a cool video! Euler was a super genius

nice I was stumped thank you.

Really like your presentation --- Thank you so much!

Incredible content. For someone whose primary math source is TH-cam it is sometimes hard to find a video that I can understand this clearly without having to check others explanations. I also watched the gamma function video and it was "diáfano" as we could say in Spanish. I wonder if you'll treat the transcendence of Euler's number someday