Math Is Fun Forum

Kenjiska

Guest

Factorial

Please,tell me the value of these-
i !
(-1) !
(1+i) !
(.1) !

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Factorial

Hi;

(-1) ! does not exist. All the negative integers of the factorial function are equal to infinity.

I would use a Taylor series for some of them. How much accuracy do you need.

Basically though you would use a computer or Wolfram Alpha to look those up. If your teacher wants to see some method then how is it you do not know that method? If I use series expansion he/she may not want that method used. So provide me with what method is to be used.

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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.

Kenjiska

Guest

Re: Factorial

Show me using the taylor series

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Factorial

Hi;

Those are all difficult but here goes nothing!

Let's try (.1)! first. For that we use a series and a trick.

It is in nested or Horner form for fast computation. The series is best for values >=5 so we put in z = 5.1

We take the exponential of both sides and get.

Now to get .1! we use a simple relation:

So

---

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.

Kenjiska

Guest

Re: Factorial

What about the others
(1+i)!
i !

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Factorial

For i! use this truncated series:

Substituting z = i you get

---

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.

zetafunc.

Guest

Re: Factorial

Also, for (1+i)!, you can find that using bobbym's answer, since