Half-precision Γ(x+1) [HP-12C]

[Albert Chan]

Very nice and compact formula, where did you get it ?
I am curious, your thread named half-precision, does a full-precision version exist ?

I rewrite below term, reduced 9 steps, all done in the stack.

\(\large c={840 x^2 + 314x + 66 \over 5040x^2 + 1464x + 419} =
{1 \over {6 - {1 \over \Large 2x + {360x+66 \over 420x-23} }}}\)

\(\Gamma(x+1) ≈ (x/e)^x \sqrt{2\pi(x+c)}\)

Code:

01- ENTER 
02- ENTER 
03- ENTER 
04- 3
05- 6
06- 0
07- ×
08- 6  
09- 6
10- +
11- X<>Y
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15- ×
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18- − 
19- /
20- +
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22- 1/X
23- CHS
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25- +
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29- 1
30- 0
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33- 1
34- 3
35- /
36- √
37- R↓
38- R↓
39- LN
40- 1
41- -
42- ×
43- eᵡ
44- ×
45- GTO 00