This program is Copyright © 1974 by Hewlett-Packard and is used here by permission. This program was originally published in the HP-65 Pac 2.
This program is supplied without representation or warranty of any kind. Hewlett-Packard Company and The Museum of HP Calculators therefore assume no responsibility and shall have no liability, consequential or otherwise, of any kind arising from the use of this program material or any part thereof.
This program approximates the value of gamma function Γ(x) for 1 < x <70.
Γ(x) =∫0...∞ tx-1e-t dt
Γ(x) = (x - 1)×Γ(x - 1)
For 1≤ x ≤ 2, polynomial approximation can be used.
Γ(x) ~ 1 + b1 (x - 1) + b2 (x- 1)2 + . . . + b8 (x - 1)8
where
b1 =-0.577191652, b2 = 0.988205891
b3 =-0.897056937, b4 = 0.918206857
b5 = -0.756704078, b6 =0.482199394
b7 = -0.193527818, b8 = 0.035868343
Note: This program can be used to find the generalized factorial x! for 0 ≤ x ≤ 69.
x! = Γ(x+ 1)
Step | Instructions | Input Data/Units | Keys | Output Data/Units |
1 | Enter program on card 1 | |||
2 | Initialize | A | ||
3 | Enter program on card 2 | |||
4 | Enter x | x | A | Γ(x) |
For a new value of x go to 4 |
Γ(5.25) = 35.21
7! = Γ(8) = 5040.00
2.34! = Γ(3.34) = 2.80
CODE KEYS 23 LBL 11 A 83 . 00 0 03 3 05 5 08 8 06 6 08 8 03 3 04 4 03 3 33 01 STO 1 83 . 01 1 09 9 03 3 05 5 02 2 07 7 08 8 01 1 08 8 42 CHS 33 02 STO 2 83 . 04 4 08 8 02 2 01 1 09 9 09 9 03 3 09 9 04 4 33 03 STO 3 83 . 07 7 05 5 06 6 07 7 00 0 04 4 00 0 07 7 08 8 42 CHS 33 04 STO 4 83 . 09 9 01 1 08 8 02 2 00 0 06 6 08 8 05 5 07 7 33 05 STO 5 83 . 08 8 09 9 07 7 00 0 05 5 06 6 09 9 03 3 07 7 42 CHS 33 06 STO 6 83 . 09 9 08 8 08 8 02 2 00 0 05 5 08 8 09 9 01 1 33 07 STO 7 83 . 05 5 07 7 07 7 01 1 09 9 01 1 06 6 05 5 02 2 42 CHS 33 08 STO 8 84 R/S 35 01 g NOP 35 01 g NOP 35 01 g NOP 35 01 g NOP 35 01 g NOP
CODE KEYS 23 LBL 11 A 41 ENTER↑ 01 1 51 - 00 0 35 24 g x>y 00 0 81 ÷ 35 07 g x⇔y 01 1 33 08 STO 8 23 LBL 02 2 35 07 g x⇔y 35 24 g x>y 22 GTO 01 1 41 ENTER↑ 41 ENTER↑ 41 ENTER↑ 34 01 RCL 1 71 × 34 02 RCL 2 61 + 71 × 34 03 RCL 3 61 + 71 × 34 04 RCL 4 61 + 71 × 34 05 RCL 5 61 + 71 × 34 06 RCL 6 61 + 71 × 34 07 RCL 7 61 + 71 × 83 . 05 5 07 7 07 7 01 1 09 9 01 1 06 6 05 5 02 2 42 CHS 61 + 71 × 01 1 61 + 34 08 RCL 8 71 × 84 R/S 23 LBL 01 1 33 STO 71 × 08 8 35 07 g x⇔y 51 - 01 1 22 GTO 02 2 35 01 g NOP 35 01 g NOP 35 01 g NOP 35 01 g NOP 35 01 g NOP 35 01 g NOP 35 01 g NOP 35 01 g NOP 35 01 g NOP 35 01 g NOP 35 01 g NOP 35 01 g NOP 35 01 g NOP 35 01 g NOP 35 01 g NOP 35 01 g NOP 35 01 g NOP 35 01 g NOP 35 01 g NOP 35 01 g NOP 35 01 g NOP 35 01 g NOP 35 01 g NOP 35 01 g NOP 35 01 g NOP 35 01 g NOP 35 01 g NOP 35 01 g NOP 35 01 g NOP 35 01 g NOP 35 01 g NOP
R1 b8 R2 b7 R3 b6 R4 b5 R5 b4 R6 b3 R7 b2 R8 used R9 used
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