Non integer factorial

• Jan 16th 2007, 06:49 AM
chogo
Non integer factorial
Hi all

First thanks alot for all the help people offer on this forum, its really well appreciated

I was wondering does anyone know how to evaluate a non integer factorial like 0.35! or 7.213!

I was thinking of using the gamma function, but how to evaluate the recursive integral numerically?

chogo
• Jan 16th 2007, 08:18 AM
CaptainBlack
Quote:

Originally Posted by chogo
Hi all

First thanks alot for all the help people offer on this forum, its really well appreciated

I was wondering does anyone know how to evaluate a non integer factorial like 0.35! or 7.213!

I was thinking of using the gamma function, but how to evaluate the recursive integral numerically?

chogo

RonL
• Jan 16th 2007, 10:41 AM
ThePerfectHacker
Quote:

Originally Posted by chogo
Hi all

First thanks alot for all the help people offer on this forum, its really well appreciated

I was wondering does anyone know how to evaluate a non integer factorial like 0.35! or 7.213!

I was thinking of using the gamma function, but how to evaluate the recursive integral numerically?

chogo

As CaptainBlank said it is Euler's Grammer Function. It is really remarkable. It has great applications in applied math.

Some interesting properties....
1) $(.5)!=\frac{\sqrt{\pi}}{2}$.
(I can prove this is you are familar with Multi-variable Calculus).

2)(For differencial equations). The generalization of the Laplace transform for the power function $y=x^n$ for $n>-1$ for non-integer values is,
$\mathcal{L} \{x^n\}=\frac{\Gamma(n+1)}{s^{n+1}}$.

This is really a remarkable function, one of my favorites (my favorite is the most ugliest function, Dirichlet Function).
• Jan 17th 2007, 03:59 AM
chogo
thanks for the help, its much appreciated.

that euler grammer function is amazing thanks!, except im writting code which should be computationally efficient

i found an approximation derived by Lanczos