Friday, August 25, 2017

TI-84 Plus CE and Casio fx-3650P: Factorial of n! and (n + 1/2)!

TI-84 Plus CE and Casio fx-3650P:  Factorial of n! and (n + 1/2)!

Factorial Formulas

The factorial for any non-negative integer n is computed by:

n! = n * (n-1) * (n-2) * … * 1
where 0! = 1

All scientific calculators with the factorial function will calculate the factorial of any positive integer up to 69 (253 for calculators with an upper limit of 10^499). 

When the factorial required for numbers in the form n/2 (example:  0.5, 1.5, 2.5, 3.5, and so on), the formula is:

(n/2)! = √π * ((n/2) * (n/2 – 1) * (n/2 – 2) * … * 1/2 )
‘where 1/2! = √π/2 ≈ 0.8862269255

When n is not an integer, we usually have to rely on the Gamma function using the relation Γ(n + 1) = n!.  This will not be covered in this post.


TI-84 Plus CE Program FACTHALF

The program FACTHALF accepts either n or n/2 as an input, where n is a non-zero integer.

"2017-08-24 EWS"
"NIST.GOV"
Disp "N! or (N/2)!"
Prompt X
If fPart(X/2)≠0.5
Then
X!→F
Else
X/2→F
Repeat X=­0.5
X-1→X
X*F→F
End
F*√(π)→F
End
Disp F

Casio fx-3650P Program for (n/2)!

The program assumes that you calculating (n/2)!.  Valid arguments are 0.5, 1.5, 2.5, etc.

(36 steps)
? → X: 1 → Y: Lbl 1: XY → Y : X -1 → X: X ≠ -.5 Goto 1:
Y √π → Y

Table of Some (n/2)! Values

0.5! = (1/2)! ≈ 0.886226925
1.5! = (3/2)! ≈ 1.329340388
2.5! = (5/2)! ≈ 3.32335097
3.5! = (7/2)! ≈ 11.6317284
4.5! = (9/2)! ≈ 52.34277778
5.5! = (11/2)! ≈ 287.8852778

Source:

“6.3.2.  What Are Variables Control Charts?”  Engineering Statistics Handbook.  http://www.itl.nist.gov/div898/handbook/pmc/section3/pmc32.htm
Retrieved August 24, 2017

Eddie


This blog is property of Edward Shore, 2017.

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