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Factorial function

  • Thread starter Pacopag
  • Start date
197
4
1. Homework Statement

I was just wondering if
[tex]n!=n(n-1)![/tex]
is completely general. Does it hold even for non-integer n?


2. Homework Equations



3. The Attempt at a Solution
 

Answers and Replies

rock.freak667
Homework Helper
6,230
31
In general, n! is only for integers.

(But it is possible to compute nCr for n being negative or a non-integer.)
 
HallsofIvy
Science Advisor
Homework Helper
41,732
893
How would you define n! for non-integer in order to have it hold?

The gamma functions, [itex]\Gamma(z)= \int_0^\infty t^{z-1} e^{-t}dt[/itex] has the property that [itex]\Gamma(z)= (z-1)![/itex] for z a positive integer, and is defined for all z except negative integers.
 

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