(12C) Stirling's approximation

10242017, 05:35 AM
(This post was last modified: 10242017 09:15 AM by Gamo.)
Post: #1




(12C) Stirling's approximation
For when you need answer from Decimal Factorial with your HP 12C
From Wikipedia: In mathematics, Stirling's approximation (or Stirling's formula) is an approximation for factorials. It is a goodquality approximation, leading to accurate results even for small values of n. Program: Code:
Example: Clear Register f [REG] [R/S] result 0 (Initialize) 2.34! > 2.34 [R/S] result 2.7976...... 4.32! > 4.32 [R/S] result 39.2945.... 5.43! > 5.43 [R/S] result 254.0337... Gamo 

11042017, 05:26 AM
(This post was last modified: 11192017 01:44 AM by Gamo.)
Post: #2




RE: (12C) Stirling's approximation
N! approximation using Forsyth's formula with shorter program steps.
Code:
Example: input N [R/S] 2.34! > 2.34 [R/S] result 2.7971...... 4.32! > 4.32 [R/S] result 39.2928.... 5.43! > 5.43 [R/S] result 254.0266... Gamo 

11042017, 02:01 PM
Post: #3




RE: (12C) Stirling's approximation
(11042017 05:26 AM)Gamo Wrote: N! approximation using Forsyth's formula with shorter program steps. Instead of 2 [y^x] you should use [ENTER] [x] which is much faster (and sometimes even more accurate). And why don't you simply use 6 [1/x] instead of 0,1667 ?) Finally, once again the ENTER is not required and should be omitted. This leads to the following version, here with a few more digits in sqrt(2pi) and without any registers: Code: ENTER This gets even a tiiiny bit closer to the true results: 2.34 [R/S] => 2.7971... 4.32 [R/S] => 39.2931... 5.43 [R/S] => 254.0287... And it accurately overflows for x > 69,95757445 Dieter 

11052017, 07:39 AM
Post: #4




RE: (12C) Stirling's approximation
Dieter Thank You
Totally forgot about 1/6 by using [ 1/x ] And your program is really improve the accuracy. Gamo 

11062017, 01:41 PM
Post: #5




RE: (12C) Stirling's approximation
(11052017 07:39 AM)Gamo Wrote: Totally forgot about 1/6 by using [ 1/x ] To be honest, the change in accuracy is negligible. The essential message was: please, do not use 2 [y^x] for squaring. [ENTER] [x] is much faster, sometimes more accurate and it even sets LastX correctly. Dieter 

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