A Tiny (WP34S) program does a lot

11282014, 03:16 PM
(This post was last modified: 11292014 11:33 AM by BarryMead.)
Post: #1




A Tiny (WP34S) program does a lot
While looking at a graph of the "Factorial" Gamma(X+1) function I noticed that between the points 0 and 1 where the value of the function is 1 (one), the function dips below one. I was curious how to find the minimum value between these two points. Using SLV with the f'(x) function made it quite easy. This tiny program illustrates how powerful a small WP34S program can be. It took only 15 program steps on the WP34S and over 40 on the HP15C.
Code:
It takes a while to run on the real WP34S (about 46 seconds), but is almost instantaneous on the emulator. Obviously when a function reaches a "Minimum" value, its first derivative (slope) will be zero. Since I don't know what the first derivative of the Factorial Gamma(X+1) looks like, I used the f'(x) function to approximate it. Note: The Optional '[Delta]X' routine helps to improve the accuracy of the result. And the answer is: 0.4616321449683623 where the factorial reaches it's minimum value of: 0.8856031944108887 Thanks to Paul Dale and Dieter for the excellent enhancements to the program. 

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