dstebbins Posted November 1, 2007 Share Posted November 1, 2007 When you perform the expression n! (read "n factorial"), you multiply all the positive integers between one and n. They have to be positive, so n>0, but they also have to be integers, so you would think that factorial of a decimal is impossible. However, when I put it into my computer's calculator, I do get a real answer. For example, .01! = 0.99432585119150603713532988870511..., and 2.1! = 2.1976202783924770541835645379483..., so there must be a way to perform a factorial of a decimal. What is it? How do you do that? Link to comment Share on other sites More sharing options...
timo Posted November 1, 2007 Share Posted November 1, 2007 My guess would be the gamma function. Link to comment Share on other sites More sharing options...
dstebbins Posted November 1, 2007 Author Share Posted November 1, 2007 ??? Link to comment Share on other sites More sharing options...
ydoaPs Posted November 1, 2007 Share Posted November 1, 2007 Gamma Function [math]\Gamma(z)=\lim_{n\rightarrow\infty}\frac{n!n^z}{z(z+1)...(z+n)}[/math] edit: 4,000th post....oh yea Link to comment Share on other sites More sharing options...
NeonBlack Posted November 1, 2007 Share Posted November 1, 2007 This is based entirely from my memory and I'm about to go to bed so CBA to verify: [math]n!=\int_0^{\infty} x^n e^{-x} dx [/math] Link to comment Share on other sites More sharing options...
Bignose Posted November 1, 2007 Share Posted November 1, 2007 The gamma function is the extension of the factorial to complex and real numbers. [math] \Gamma(n) = (n-1)![/math] and the Gamma function is defined as: [math]\Gamma(n) = \int_0^{\infty} t^{n-1}e^{-t} dt [/math] You can see a lot more at Mathworld: http://mathworld.wolfram.com/GammaFunction.html Link to comment Share on other sites More sharing options...
timo Posted November 1, 2007 Share Posted November 1, 2007 The gamma function is the extension of the factorial to complex and real numbers. It is an extension (admittedly the commonly-mentioned one, hence my guess). Link to comment Share on other sites More sharing options...
Dave Posted November 2, 2007 Share Posted November 2, 2007 Also, you should note that the Gamma function is not defined for any negative integer (I believe there are poles at each one of those points). Link to comment Share on other sites More sharing options...
the tree Posted November 2, 2007 Share Posted November 2, 2007 Can't say I understand what a factorial of a non-natural number would mean. I always understood that the definition was the amount of ways to order n objects and any formula was merely a way of calculating that. And ways to order 2.5 distinct objects doesn't make much sense to me. Although I guess I could have it very backwards. Link to comment Share on other sites More sharing options...
Country Boy Posted November 4, 2007 Share Posted November 4, 2007 Can't say I understand what a factorial of a non-natural number would mean.I always understood that the definition was the amount of ways to order n objects and any formula was merely a way of calculating that. And ways to order 2.5 distinct objects doesn't make much sense to me. Although I guess I could have it very backwards. No, you are correct- the "factorial" is only defined for positive itegers. What others are saying here is that the "gamma function" has the property that it is identical to the factorial for positive integer values of the argument but is defined for other numbers as well. (It is NOT defined for negative integers because the integral does not exist in that case.) Link to comment Share on other sites More sharing options...
Gyana Ranjan Nayak Posted July 5, 2023 Share Posted July 5, 2023 (edited) I slove it in 2020 on pen and paper how exactly slove it. can I upload the solution?? Edited July 5, 2023 by Gyana Ranjan Nayak Link to comment Share on other sites More sharing options...
Genady Posted July 5, 2023 Share Posted July 5, 2023 (edited) In the 15 years since this thread was inactive good explanations have been added, for example, in youtube: Edited July 5, 2023 by Genady Link to comment Share on other sites More sharing options...
Gyana Ranjan Nayak Posted July 6, 2023 Share Posted July 6, 2023 (edited) Decimal factorial.pdf Edited July 6, 2023 by Gyana Ranjan Nayak Link to comment Share on other sites More sharing options...
joigus Posted August 5, 2023 Share Posted August 5, 2023 On 7/6/2023 at 12:22 PM, Gyana Ranjan Nayak said: Decimal factorial.pdf 165.54 kB · 5 downloads This calculation seems to be correct. Just in case anybody's interested, and because this thread has recently been revived, there's another definition that overlaps with that of a factorial (or gamma function). Namely, the falling and rising factorials. Although it's a generalisation in a different sense. The variable is not the "n" in n! Link to comment Share on other sites More sharing options...
Recommended Posts
Create an account or sign in to comment
You need to be a member in order to leave a comment
Create an account
Sign up for a new account in our community. It's easy!
Register a new accountSign in
Already have an account? Sign in here.
Sign In Now