The Inverse Factorial? (Using Stirling's Approximation!)

0:00 Introduction
0:16 Stirling's Approximation
1:26 Using a Limit to Show That the New Form Works
2:16 Solving For x
7:20 Plugging Values Into Derived Equation

[AshtonM]

This video saved my programming assignment. Thanks!

[neomooooo]

The “Stirling formula” was actually due to De Moivre. The alternative you switch to is in fact due to Stirling, and is more accurate. Unfortunately the math literature has been propagating the mislabeled formula for centuries now, and there is little hope in correcting the misnomer.

Great video, keep up the good work!

[Charles_Reid]

Great vid! I wish they taught the lambert W function in highschool. It seems like it’s so powerful and that it comes up pretty often when doing algebra.

[DanTheManHibiki]

I may have found a closed form for the Lambert function you used in my book, Mathematical Flirtations. Thank you for Sterling’s Approximation, I wasn’t aware of that one!

[mathadventuress]

Divide by ! To get x=100/! :) thanks for watching my Ted talk

[ShiroIsNotKuro]

Great video! Very clear and methodological explanation!

[Nolord_]

Wow, very original Idea and pretty cool to solve

[allozovsky]

07:27 _In Wolfram Alpha, if you want the Lambert W function, you write in "productlog"_
Typing "LamberW" or simply "W" will normally do as well – WA will just show you a warning "Assuming "W" is a math function | Use as a unit instead" and explain below that "W(z) is the product log function".
Also you can specify the branch (as the first argument) and, say, find a real-valued solution to the equation x^x = 1/4 in the following way: exp(W(−1, ln(0.25) + 2 I Pi)) which will give you x = −2, as expected.

[ChrisElCrack]

Amazing video. Keep up the good work, you’re gonna make it far ❤️

[elliottmanley]

Worth mentioning that 4.893 is only the principal solution. There are also negative solutions.

[UberHummus]

Could be a dope follow up to show how the factorial equation is solved/the interpretation of a factorial of a non-integer number

[elliottmanley]

That's a neat trick, inverting the gamma function without ever mentioning it :)

[Arthur-socd]

is this a factorial function? nice video

[bontdor]

X!=st(x)=(x/e)^x*sqrt(2*pi*x) stirling Approximation denoted by st(x) , if you took x!=gamma(x+1)=st(x)*e^y, where power of e=2.71828182846 is you get 5 decimals of x! For x in interval [2, 9] so try to inversate

[arberithaqi]

Does the estimated equation gets closer to the real solution, if x gets bigger, or is it random?

[silasrodrigues]

Did the square root of 2*PI just disappeared?
I didn't get it why it went 2*PI without root...

[damianmedina]

Thinking about CS and wondering at what point (how large of a number) is it not worth it to just use a for loop to solve this problem? And when the number is that large, the factorial result is so large that it makes me wonder: what are we even looking at here? Is this a number that we care about from a practical/applied sense?

[somerandomvideos]

1/5 th finalist maths master is you, Congratulations.

[djridoo]

Hello,
It's a great video, but I don't see the difference between doing the calculation with a computer at the beginning and the end
Have a good day

[the-ercd]

Hey, awesome. Have you thought of doing these digitally, (I'm not saying this isn't good!)