Lambert W Function (hp-42s)

[Albert Chan]

This gives exp(W(a)), which equals a / W(a)

Code:

00 { 33-Byte Prgm }
01▸LBL "eW"
02 LSTO "a"
03 1
04 +
05▸LBL 01
06 ENTER        ; y     y
07 RCL+ "a"     
08 LASTX        ; y     a+y     y
09 LN
10 1
11 +
12 ÷            ; y'    y
13 -            ; eps
14 LASTX        
15 X<>Y         ; eps   y'
16 X↑2
17 X<>Y         ; y'    eps^2
18 +
19 LASTX        ; y'    y'+eps^2
20 X≠Y?
21 GTO 01
22 END

Example, for i^i^i ...

-1
SQRT
LN
+/-
XEQ "eW"
1/X

→ 0.438282936727 + 0.360592471871 j