(28/48/50) Lambert W Function

[Gil]

I tried to translate your code in post 17, Albert.

{ "« x -.1 <=
IF
THEN .367879441171 'R' STO 4.42321595524E-13 'R2' STO 'sqrt(2.*R*(x+R+R2))*(k+k+1.)' —>NUM 'Y' STO 'R+Y*sqrt (1.+Y/(3.*R))' —) NUM 'Y' STO
DO Y 'Y+x' '(Y-R-R2)/R' —>NUM DUP TYPE 1. ==
IF
THEN 1. + LN
ELSE LNP1
END / - —>NUM 'H' STO 'Y-H' —>NUM 'Y' STO Y 'Y+H*.0001' —>NUM ==
UNTIL
END
ELSE 'k+k+1.' '(k+k+1.)*x/4.' + —>NUM 'Y' STO
DO 'Y-(Y+x)/(LN(Y)+1.)' —>NUM 'H' STO 'Y-H' —>NUM 'Y' STO
UNTIL Y 'Y+H*.0001' —>NUM ==
END
END x Y /

»-x =-.36787944118
W(k=->; (-.999999999985,-6.87304618656E-6)

Result ± ok for imaginary part.

Your translated code for more accuracy, post 19, same input values
« x -.1 ‰
IF
THEN .367879441171 'R' STO 4.42321595524E-13 'R2' STO '(x+R+R2)/R' —>NUM 'H' STO 'sqrt(2.*H)*(2.*k+1.)' —>NUM 'X' STO 'X*sqrt(1.+X/3.)' —>NUM 'X' STO 'R+R*X' —>NUM 'Y' STO
DO X DUP TYPE 1. ==
IF
THEN 1. + LN
ELSE LNP1
END 'Z' STO 'X-(X-Z+H)/Z', —>NUM 'Z' STO X Z - 'X' STO X 'X+Z*.000001' —>NUM ==
UNTIL
END X DUP TYPE 1. ==
IF
THEN 1. + LN
ELSE LNP1
END 1. -
ELSE 'k+k+1.' '(k+k+1.)*x/4.' + —>NUM 'Y' STO
DO 'Y-(Y+x)/(LN(Y)+1.)' —>NUM 'H' STO 'Y-H' —>NUM 'Y' STO
UNTIL Y 'Y+H*.0001' —>NUM ==
END x Y /
END
»

No solution is found: X is never equal to 'X+Z*.000001'.

Why this difference of "behaviour"?

And why, in code post 29, did you define Y=R+R*X, that seems never to be used again?