Talk:Factorial

An imperative way of calculating factorial may be more understandable. In Python code:

def fact(x):
    result = 1
    while x > 1:
        result *= x   # multiply result by x
        x -= 1        # decrease x by 1
    return result

Moved from the article. Is this really worth mention? -- Taku 21:38 Apr 25, 2003 (UTC)

Derivative of the factorial

Does anyone know some values of the function that can be recieved by differentiating the factorial, using the ? symbol for this function?? A graphing calculator can be helpful. Try to see if you know the values of:

1? =
2? =
3? =
4? =
5? =
6? =
7? =
8? =
9? =
10? =

Dou you see a pattern for the values of n? for the integers?? (Look! We now have a mathematical meaning for just about every symbol on the computer; any counterexamples??)

How can you differentiate the factorial when it isn't a continuous function? You could differentiate the gamma function, though. Eric119 22:41, Jun 30, 2004 (UTC)

It's continuous over certain intervals. It just has pole as non-positive integers. Its not continuous, but its still differentiable. He Who Is 01:06, 6 June 2006 (UTC)[reply]

Wouldn't it be better to mention the integral definition

z!=\int _{0}^{\infty }e^{-t}t^{z+1}\,dt

in the discussion of the gamma function? 4pq1injbok 02:32, 16 Jul 2004 (UTC)

No, it has obvious relevance here also. Dysprosia 02:38, 16 Jul 2004 (UTC)

Sure, but isn't it still primarily about the gamma function? After all, the factorial is discrete, so defining it for nonintegral arguments is essentially defining the gamma function. It seems a bit scattered to me to talk about nonintegral z in two distinct places. 4pq1injbok 21:27, 16 Jul 2004 (UTC)

Is there a term for the sum of positive integers less than or equal to the given number? Bless me if I can't find reference to one.

Yes, a triangular number. --- User:Karl Palmen 5 August 2004

Adding an external link: http://www.luschny.de/math/factorial/FastFactorialFunctions.htm This site shows several interesting algorithms to compute the factorial.

Incorrect reference to "the above recursive relation"

"Proper attention to the value of the empty product is important in this case, because <...> it makes the above recursive relation work for n = 1;"

But the recursive relation is given at the end of the next section (Applications), not above.

Superfactorials

Superfactorials get large very rapidly. Between what two consecutive superfactorials does Graham's number lie?? 1$ = 1 and 2$ = 4, but even 3$ is too big to write; it is 6^6^6^6^6^6. 66.32.244.149 21:43, 2 Nov 2004 (UTC)

factorials for halves?

How does one calculate factorials that are in the form (n + .5)!, where n is a whole number? On windows calculator, it says 3.5! = 11.631728396567448929144224109426. how is this calculated?

With the gamma function. Fredrik | talk 02:59, 9 Feb 2005 (UTC)

Yup, 3.5! is the same as Γ(4.5). --MarkSweep 06:19, 9 Feb 2005 (UTC)

Strange... The Windows calculator returns about 0.88 as .5!, which is less than 1 and clearly not sqrt(pi)... He Who Is 00:51, 6 June 2006 (UTC)[reply]

Looks right to me. 0.5! = Γ(1.5) = 0.5 Γ(0.5) = √π / 2 = 0.88623... —Steven G. Johnson 00:59, 6 June 2006 (UTC)[reply]

Ahhh... I forgot about the phase change between factorials and gammas, and interpereted Γ(.5) as root pi. I've always wondered why the gamma function is more commonly used in evaluating factorials. The Pi function has no phase change and a slightly simpler formula, so why does everyone opt for the one that requires more work? He Who Is 01:02, 6 June 2006 (UTC)[reply]

Fast computation

Luschny's "prime swing" algorithm is quite neat. I've translated his source code into Python/gmpy, and found it to be four times faster than Mathematica's n! and twice as fast as gmp's built-in factorial (testing with n up to 1000000). The algorithm is unfortunately poorly documented, so there doesn't seem to be much hope for writing about it here. Anyone here with more knowledge about this? Fredrik | t c 13:53, 25 November 2005 (UTC)[reply]

Factorials for Fun

I've seen numerous videos and countless images using factorials utalizing their unique designs. Someone should make a section with a picture maybe showing this. 65.9.89.94 03:46, 2 March 2006 (UTC)[reply]

What "designs" are you referring to? Michael Hardy 20:04, 2 March 2006 (UTC)[reply]

Identities

Some identies for evaluating the factuarials of common binary functions would make a good addition to this article. For instance:

$(a+b)!={\frac {a!b!}{|b-a|!}}$

Or hopefully something without the recursivity in the denomitator. He Who Is 00:59, 6 June 2006 (UTC)[reply]

I don't think you mean that. For example if a=3 and b=4, you would get (a+b)!=5040 while the right hand side would be 6*24/1. --Audiovideo 22:22, 21 June 2006 (UTC)[reply]