Incomplete Gamma Function

[Namir]

This program implements an incomplete Gamma function base don an HP-25 program by Peter Henrici.

Memory Map

R0 = X
R1 = A
R2 = L(n-2)
R3 = L(n-1)
R4 = s
R5 = gamma(n)
R6 = n
R7 = tolerance

Listing

Code:

1 LBL a
2 STO 7
3 R/S
4 LBL A
5 STO 1
6 X<>Y
7 STO 0
8 CLX
9 STO 2
10 STO 4
11 1
12 STO 3
13 STO 6
14 RCL 1
15 RCL 0
16 Y^X
17 STO 5
18 RCL 1
19 EXP
20 STO/ 5
21 LBL 0
22 RCL 5
23 RCL 6
24 RCL 0
25 -
26 STO* 5
27 1
28 -
29 RCL 3
30 RCL 2
31 -
32 *
33 RCL 6
34 RCL 1
35 +
36 RCL 3
37 STO 2
38 *
39 +
40 RCL 6
41 /
42 STO 3
43 RCL 2
44 *
45 /
46 STO+ 4
47 PAUSE
48 ABS
49 RCL 7
50 X<>Y
51 X<=Y?
52 GTO 1
53 1
54 STO+ 6
55 RCL 6
56 STO/ 5
57 GTO 0
58 LBL 1
59 RCL 4
60 R/S
61 GTO A

Usage


1. Enter the tolerance value and press [f][A]. The program automatically resumes with step 2.
2. Enter the values for A and X, and then press [A].
3. The program pauses to display the improvements in the calculated incomplete gamma function. When these improvements are less than the tolerance value, the program displays the result. If you press [R/S] after viewing the value of the incomplete gamma, the program flow resumes with step 2.