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#1 2012-10-25 13:46:44

Kenjiska
Guest

Factorial

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

#2 2012-10-25 15:45:29

bobbym
Administrator

Online

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.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#3 2012-10-25 19:19:34

Kenjiska
Guest

Re: Factorial

Show me using the taylor series

#4 2012-10-25 20:43:25

bobbym
Administrator

Online

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.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#5 2012-10-25 21:45:46

Kenjiska
Guest

Re: Factorial

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

#6 2012-10-25 22:41:49

bobbym
Administrator

Online

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.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#7 2012-10-26 03:25:29

zetafunc.
Guest

Re: Factorial

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

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