An elegant proof of Legendre's duplication formula for the gamma function

[@manstuckinabox3679]

I don't care if it's a reupload, if it's a Maths 505 vid, I'm watching it

[@maths_505]

Thanks bro😂 I had to reupload it cuz of audio issues with the first one

[@marc1310]

When I was 17 years old, I proved this Legesdre's duplication formula using the definition of the factorial (n!=n(n-1)(n-2)...1). Of course I got help from the internet about some other definitions. It was so extended! I felt proud of my result and I used websites like geogebra or desmos to confirm what I got. Now I am 21 years old, but unfortunately I cannot go to the University because of personal reasons.

[@maths_505]

It's cool....I had to teach myself almost all of this stuff too

[@wizz_larza]

im preparing for JEE exam, but... not gonna lie i love maths, specially these MIT, BMT, and Maths 505 intregals... im 16 and watching your videos i could expand my research on a specific function or lets say.. an infinite product... when i started, i didn't know much about gamma, diagamma, trigamma, beta, reimann zeta function etc.. not even knowing about infinite series or intregals... infinite product was quite so far hahah.. i realized a beautiful pattern in maths.. x! x^x , that is (x-1)! x^x+1 and much more memories to this function in my journey of learning deeply about one to one, onto, range, codomain etc by myself ;) depressed times.. those when i lost the love of my life... 😔

[@KramRemin]

Continue to do math privately, and mind you don't get killed in a duel.

[@maths_505]

@KramRemin legendary advice 🔥🔥

[@KramRemin]

@@maths_505 Yo Kamal, Still fussing over the 2/28 video. ("The worst calculus problem I've ever solved (or is it one of the best?)") For me, it works out like the ticks on a ruler, 3 binary processes in competition. At each step, there are twice as many "buildings," but they're half as wide and half as tall. I fired up my high-tech ball-point pen graphics technology to draw a picture: kzbin.info/www/bejne/gqGceXmrlsyJhZY

[@azmath2059]

Magnificent as always

[@slavinojunepri7648]

This is Math in its purest form

[@skyethebi]

Can you do a video proving the relationship between the gamma and beta function?

[@michaelguenther7105]

I'd love to see you prove Gauss' multiplication formula, the generalization of the duplication formula for Gamma[kz].

[@davidblauyoutube]

Very nice!

[@maths_505]

Thanks mate

[@skyethebi]

5:54 real math chads do φ-subs

[@tfg601]

I thought it was the gamma(z) * gamma(z+1/2) = (sqrt(pi) * gamma(2z))/(2^{1-2z}) where it is division by 2^(1-2z)