Solution 11749: Factorials of Decimal (0.5) Numbers on Texas Instruments Graphing Calculators.
Why do I get an answer when I factor numbers ending in .5 on my graphing calculator?
Factorial is defined as:
The factorial is computed recursively using the relationship, (n+1)! = (n+1)*n!, until n is reduced to either 0 or -1/2. At this point, the definitions, 0! = 1 or (-1/2)! = (p), are used to complete the calculation.
n! = n*(n-1)*(n-2)*...*2*1, if n is an integer >= 0
n! = n*(n-1)*(n-2)*...*1/2*(p), if n + 1/2 is an integer >= 0
n! is an error otherwise.
The reason 1/2 factorials are allowed:
Computation of the pdf's and cdf's for the t, F and c2 distributions involve the use of the g function. When one is dealing with a single degree of freedom for one of these functions, one must compute g(1/2), which is equivalent to (-1/2)!. Hence, providing the ability to do half factorials provides users with the ability to duplicate the pdf computations provided, without having to invent their own factorial or g function. Since degrees of freedom never go below 1, there is no need for anything smaller than (-1/2)!.