Education Technology

Solution 11957: Calculating Factorials (!) of Rational Numbers on a TI-83 Family, TI-84 Plus Family, TI-84 Plus C Silver Edition or TI-Nspire™ Handheld in TI-84 Plus Mode.

How do I calculate (!) factorials of rational numbers on a TI-83 family, TI-84 Plus family, TI-84 Plus C Silver Edition or TI-Nspire in TI-84 Plus mode?

The factorial (!) is computed recursively using the relationship, (n+1)! = (n+1) 4 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. Hence:

n! = n 4 (n-1) 4 (n-2) 4 ... 4 2 4 1, if n is an integer >= 0
n! = n 4 (n-1) 4 (n-2) 4 ... 4 1/2 4 p, if n + 1/2 is an integer >= 0
n! is an error otherwise

Computation of the pdf's and cdf's for the t, F, and c2 distributions involve the use of the gamma function G(n). When 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 by a TI-83 family, TI-84 Plus C Silver Edition or TI-84 Plus family graphing calculator, without having to invent their own factorial or gamma function.

Since degrees of freedom never go below 1, there is no need for anything smaller than (-1/2)!.

Please see the TI-83 family, TI-84 Plus C Silver Edition and TI-84 Plus family guidebooks for additional information.

Note: TI-Nspire handheld in TI-84 Plus mode users may refer to the TI-84 Plus family guidebook