integral competition HP50g vs. DM42

[JMBaillard]

Hi !
here is an HP41 version that employs an ascending series for small x
and a complex continued fraction otherwise:

01 LBL "CSX"
02 STO 01
03 ABS
04 PI
05 SQRT
06 X>Y?
07 GTO 04
08 DEG
09 *
10 24
11 STO 02
12 CLX
13 2
14 /
15 STO 03
16 ENTER
17 LBL 01
18 X<>Y
19 CHS
20 STO Z
21 X^2
22 RCL Y
23 X^2
24 +
25 DSE 02
26 X<0?
27 GTO 02
28 RCL 02
29 X<>Y
30 ST+ X
31 /
32 ST* Z
33 *
34 RCL 03
35 ST+ Z
36 +
37 GTO 01
38 LBL 02
39 PI
40 SQRT
41 *
42 ST/ Z
43 /
44 R-P
45 RCL 01
46 X^2
47 90
48 *
49 R^
50 -
51 X<>Y
52 CHS
53 P-R
54 1
55 +
56 STO Z
57 X<>Y
58 ST+ Z
59 -
60 2
61 ST/ Z
62 /
63 GTO 05
64 LBL 03
65 X<> 00
66 PI
67 2
68 ST+ 02
69 /
70 RCL 01
71 X^2
72 *
73 X^2
74 *
75 RCL 02
76 ENTER
77 DSE X
78 *
79 /
80 CHS
81 STO 00
82 RCL 02
83 ST+ X
84 ISG X
85 CLX
86 /
87 X<>Y
88 ST+ Y
89 X#Y?
90 GTO 03
91 RTN
92 LBL 04
93 CLX
94 STO 02
95 X<>Y
96 STO 00
97 ENTER
98 XEQ 03
99 STO 03
100 1
101 STO 02
102 RCL 01
103 ABS
104 3
105 Y^X
106 PI
107 *
108 2
109 /
110 STO 00
111 3
112 /
113 ENTER
114 XEQ 03
115 RCL 03
116 LBL 05
117 RCL 01
118 SIGN
119 ST* Y
120 ST* Z
121 RDN
122 END

Example:

1.2 XEQ "CSX" >>>> C(x) = 0.715437723
X<>Y S(x) = 0.623400918

3.9 R/S >>>> C(x) = 0.422332710
X<>Y S(x) = 0.475202402

Best regards.