Math Is Fun Forum

hussam

Member

Registered: 2015-04-06

Posts: 46

x!

hi everyone;

I know that 3!=3*2*1    4!=4*3*2*1 ........

but how can i calculate (0.5)! or (0.2)!  ?

my calculator show me that (0.5)!=1   and (0.2)!=1

is there a rule to calculate X! : (x isn't a natural number)?

phrontister

Real Member

From: The Land of Tomorrow

Registered: 2009-07-12

Posts: 4,882

Re: x!

Hi hussam,

My hand-held HP 32SII calculator gives:
    0.5! = 0.886226825453
    0.2! = 0.9181687424

My Windows 8 scientific calculator gives the same result, but to more decimal places.

MIF has a page here about factorials.

Non-integer factorials are mentioned near the bottom of the page:

What About Decimals?

Can we have factorials for numbers like 0.5 or -3.217?

Yes we can! But we need to get into a subject called the "Gamma Function", which is beyond this simple page.

It's also beyond simple me!

Last edited by phrontister (2015-04-10 19:44:14)

---

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: x!

Hi;

There are a couple of ways. One is by direct calculation and the other is by a series.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

hussam

Member

Registered: 2015-04-06

Posts: 46

Re: x!

thank you  phrontister , bobbym

Last edited by hussam (2015-04-10 19:58:39)

phrontister

Real Member

From: The Land of Tomorrow

Registered: 2009-07-12

Posts: 4,882

Re: x!

Hi Bobby,

Could you explain those two methods for me, please?

Thanks.

---

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: x!

Supposing you wanted to know what 5.3! is amd you knew what .3! was. You can then use this method.

.3! (5.3) (4.3) (3.3) (2.3) (1.3) = 5.3!

Now how do you get .3! if you do not know it? For that, you use a Taylor series. M can generate them for you. There is also an integral but it is not much use for computation.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

phrontister

Real Member

From: The Land of Tomorrow

Registered: 2009-07-12

Posts: 4,882

Re: x!

Thanks for that, Bobby, but it's getting a bit heavy and so I think I'll quit with that.

I understand how your equation works, and that it follows the rule that MIF mentioned on the page I gave the link to in my first post: viz, that "the factorial of any number is that number times the factorial of (1 smaller than that number)".

At least I now know that non-integer factorials exist, which may come in handy for something. I was surprised that they did, though, because I tried it a little while back on two scientific calculators I use a fair bit and got an error on both. Anyway, M, W8 and my HP can do it.

---

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: x!

M is the mightiest force in the galaxy. Master it and you will stand alone.

but it's getting a bit heavy

Do not worry about heavy, M is very strong and can carry bloated math jargon easily.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

ishwar

Member

Registered: 2015-04-12

Posts: 2

Re: x!

hi hussam
I can help you out with (0.5)! since according to the Gamma Function,(-0.5)! is square root (pi).
Now you can times by 0.5 because it is 1 more than -0.5. So (0.5)!=square root pi divided by 2.
you can continue this for (1.5)! or (2.5)! and so on. And by the way, (5.5)! is (10395* square root pi)/64.

hussam

Member

Registered: 2015-04-06

Posts: 46

Re: x!

Thank you  ishwar , the first post for you is to help me ! thank you .