Uselessness!
Dec. 17th, 2003 10:03 pm![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png){kind=small}
sniffnoyOpen up Windows calculator (assuming you're on a Windows machine). Go to scientific view (if it's not already!). Enter -1/2. Hit factorial. Square.
You ought to notice a few things:
1. Hitting factorial does not produce an error - Windows calculator apparently has some way of calculating "factorials" of fractional values. This was something I noticed long ago, long before I ever heard about the gamma function. But do these values indeed match Γ(x+1)?
2. They do indeed. Or at the very least, they do for x =-1/2. Because you'll notice the number you get after hitting factorial is positive, and the number you get after squaring is pi (or, subtracting pi, it is to 32 decimal places) - ie, it is √π, which, for reasons I don't know (but Mathworld and Wikipedia say so), equals Γ(1/2), ie, Γ(-1/2+1). So I'd say it's pretty probable that...
Windows Calculator uses the gamma function, at least partly, to calculate factorials!
Is that amazing and useless, or what?
-Sniffnoy
--
When trying the fact that " quite simple what is designed completely
too little we should do to estimate the device of the common mistake
complete idiot. " - The harmless Douglas Adams, mostly
(Everyone loves Babelfish!)
You ought to notice a few things:
1. Hitting factorial does not produce an error - Windows calculator apparently has some way of calculating "factorials" of fractional values. This was something I noticed long ago, long before I ever heard about the gamma function. But do these values indeed match Γ(x+1)?
2. They do indeed. Or at the very least, they do for x =-1/2. Because you'll notice the number you get after hitting factorial is positive, and the number you get after squaring is pi (or, subtracting pi, it is to 32 decimal places) - ie, it is √π, which, for reasons I don't know (but Mathworld and Wikipedia say so), equals Γ(1/2), ie, Γ(-1/2+1). So I'd say it's pretty probable that...
Windows Calculator uses the gamma function, at least partly, to calculate factorials!
Is that amazing and useless, or what?
-Sniffnoy
--
When trying the fact that " quite simple what is designed completely
too little we should do to estimate the device of the common mistake
complete idiot. " - The harmless Douglas Adams, mostly
(Everyone loves Babelfish!)
