This is nice. Another way is to take the Laplace transform of t^n and then set s=1. This gives an integral representation for n! You can then use the integral to define factorials for other real and complex numbers, other than the negative integers. Edit: that’s basically what you did of course, but it means you can skip to that last step :-)
This is a really good video!! I love the spirit of *actually deriving* than just showing that a given known result works. This made my day
I click because I was wondering why gamma is shifted by 1 relative to factorial
I might be stupid, but in 5:30 onwards, wouldn't plugging in t=infinity for e^xt/x just give infinity rather than 0?
My first time rly understanding gamma function and getting an intuitive grasp of it thx man never forget your favor❤
i was wondering where you were
Just went away for 2 weeks and found myself without internet connection. I would never leave you!
I've been looking for a derivation of this mysterious function for absolutely ages, thank you so much for this video
This is so cool
Enjoyed! great work.
Amazing😄😇
Have you done a video on Calculus of Variations, and the Euler Lagrange equation? If not could you cover it?
Very cool derivation
This is nice. Another way is to take the Laplace transform of t^n and then set s=1. This gives an integral representation for n! You can then use the integral to define factorials for other real and complex numbers, other than the negative integers.
Edit: that’s basically what you did of course, but it means you can skip to that last step :-)
Wow