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Gerson W. Barbosa · (This post was last modified: 12-11-2017 02:23 PM by Gerson W. Barbosa.)

The 12C program is more obsfuscated than it need be because I was trying to save one step or two, which I could not. Here is an equivalent 32S II listing, for the sake of clarity:

G01 LBL G
G02 ENTER
G03 ENTER
G04 ENTER
G05 36
G06 *
G07 12.5
G08 +
G09 *
G10 5
G11 +
G12 1/x
G13 2
G14 +
G15 *
G16 3
G17 1/x
G18 +
G19 PI
G20 *
G21 SQRT
G22 x<>y
G23 ENTER
G24 y^x
G25 *
G26 x<>y
G27 e^x
G28 /
G29 RTN

CK=AE97 053.0

This is based on formula 27 here, slightly modified to improve accuracy.

PS: These make things more clear:

Plot [(√(((2+1/(36*x^2+25/2*x+5))*x+1/3)*π)*x^x/e^x - Γ(x+1))/Γ(x+1)], x=1/100..1

Plot [(√(((2+1/(36*x^2+25/2*x+5))*x+1/3)*π)*x^x/e^x - Γ(x+1))/Γ(x+1)], x=1..60

Now, let us compare the latter result with the one given by the original formula:

Plot [(√((2*x+1/3)*π)*x^x/e^x - Γ(x+1))/Γ(x+1)], x=1..60