Digamma Function for the free42

[Juan14]

The next program uses the formula provided by Albert Chan here. The program shifts the argument value 35 units to improve precision and then by the recurrence formula ψ(x+1)=ψ(x)+1/x calculates the desired value. The values I obtained seem to be accurate in the first 15 digits. It would be interesting if some one can try it in the original hp 42s.

PHP Code:

00 { 73-Byte Prgm }
01 LBL “Psi”
02 STO 11
03 34.5
04 +
05 74381
06 689976
07 RCL× ST Z
08 ÷
09 10
10 37
11 ÷
12 RCL× ST Z
13 +
14 1/X
15 24
16 RCL× ST Z
17 +
18 1/X
19 +
20 LN
21 35
22 X<>Y
23 LBL 00
24 -1
25 RCL+ ST Z
26 RCL+ 11
27 1/X
28 -
29 DSE ST Y
30 GTO 00
32 END