(41) Γ(x+1) [HP-41C]

[Gerson W. Barbosa]

.
HP-41C:

01 LBL "GXP1"
02 1
03 STO 01
04 SF 05
05 X<>Y
06 X<=0?
07 X=0?
08 GTO 01
09 CF 05
10 STO 02
11 CHS
12 LBL 01
13 4
14 STO Z
15 X<=Y?
16 GTO 03
17 +
18 RCL X
19 1
20 +
21 LBL 02
22 1
23 -
24 ST* 01
25 DSE Z
26 GTO 02
27 LBL 03
28 X<>Y
29 4.13333
30 2.215
31 RCL Z
32 *
33 .4875
34 -
35 R^
36 X^2
37 /
38 +
39 12
40 /
41 +
42 72
43 *
44 1/X
45 6
46 1/X
47 +
48 +
49 360
50 D-R
51 *
52 SQRT
53 X<>Y
54 1
55 E^X
56 /
57 R^
58 Y^X
59 *
60 RCL 01
61 /
62 FS? 05
63 GTO 04
64 PI
65 RCL 02
66 *
67 X<>Y
68 LASTX
69 -1
70 ACOS
71 *
72 SIN
73 *
74 /
75 LBL 04
76 END

117 BYTES

———————-

-69.95 -> -1.450781639E-97 {0 ULP}
-2.5 -> 2.36327180(1) [4/3×√π] {1}
-2.0 -> DATA ERROR
-1.5 -> -3.544907(697) [-2√π] {5}
-1.0 -> DATA ERROR
-0.5-> 1.7724538(47) [√π] {4}
0 -> 1.00000000(1) {1}
.5-> .88622692(77) [√(π/4)] {22}
1 -> 1.00000000(1) {1}
2 -> 1.999999999 {1}
3 -> 6.0000000(12) {12}
4 -> 24.0000000(3) {3}
5 -> 119.999999(5) {5}
6 -> 719.999999(5) {5}
7 -> 5040.0000(10) {10}
8 -> 40320.0000(6) {6}
9 -> 362880.000(4) {4}
10-> 3628800.00(2) {2}
11-> 39916800.(11) {11}
12-> 47900160(1.1) {11}
13-> 62270208(12) {12}
14-> 87178291(32) {12}
15-> 1.3076743(73)E12 {5}
20-> 2.4329020(18)E18 {10}
30-> 2.652528(633)E32 {35}
50-> 3.0414093(32)E64 {12}
60-> 8.3209871(07)E81 {6}
69-> 1.7112245(67)E98 {43}
69.95 -> 9.682847673E99


———————-



HP-75C:

10 INPUT X
15 P=1 @ Q=0
20 IF X<0 Q=1 @ W=X @ X=-X
25 IF X<4 THEN X=X+4 @ P=X*(X-1)*(X-2)*(X-3)
30 C=62/15-443/(200*X)-39/(80*X*X)
35 Z=(6*X+1+1/(12*X+C))/6
40 F=SQR(2*Z*PI)*(X/EXP(1))^X/P
45 IF Q THEN F=W*PI/(F*SIN(W*ACOS(-1)))
50 D=DISP F

————-

-253.11 -> -2468119655(10)E-497 {2 ULP}
-71.06 -> -1.084216232(55)E-99 {11}
-2.5 -> 2.363271801(91) [4/3×√π] {70}
-2.0 -> -9.99999999999E499 [-∞]
-1.5 -> -3.54490770(200) [-2√π] {19}
-1.0 -> -9.99999999999E499 [-∞]
-0.5-> 1.772453850(91) [√π] {76}
0 -> 1.0000000000(3) {3}
.5-> .886226925(833) [√(π/4)] {380}
1 -> 1.0000000000(2) {2}
2 -> 1.999999999(61) {39}
3 -> 5.99999999(801) {199}
4 -> 24.00000000(73) {73}
5 -> 120.0000000(24) {24}
6 -> 719.999999(860) {140}
7 -> 5039.99999(833) {167}
8 -> 40319.9999(865) {135}
9 -> 362879.999(892) {108}
10-> 3628799.999(06) {94}
11-> 39916799.99(15) {85}
12-> 479001599.9(26) {74}
13-> 6227020799.(21) {79}
14-> 87178291(190.7) {93}
15-> 1.30767436(787)E12 {13}
20-> 2.432902008(10)E18 {8}
30-> 2.65252859(778)E32 {34}
50-> 3.041409320(40)E64 {23}
60-> 8.32098711(301)E81 {27}
69-> 1.711224524(14)E98 {14}
69.95 -> 9.68284767(192)E99 {108}
253.1 -> 8.998861511(22)E499 {23}

ANGLE OPTION DEGREES

For better accuracy in radians mode change line 45 to

45 IF Q THEN F=W*PI/(F*SIN(MOD(W,2)*ACOS(-1)))

per Albert Chan’s suggestion above.

For best 12-digit results change line 30 to

30C=4.1332883071+2.1999058932/X-.3505828048/(X*X)-.2950235942/X^3
————-

Edited to fix a few typos.