# 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?

I welcome any advice

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?

I welcome any advice

chogo

As always the Wikipedia page is a good place to start.

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?

I welcome any advice

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

i cant for the life of me understand that, but perhaps one of you guys might be interested. I think ill just stick with using eulers function even though it may be computationally inefficient

thanks again guys