HP49-50G,VER16.2 Lambert Funktion Wk(x), k=k= 0, ±1, ±2, ±3, ±4..., x real or complex

[Gil]

New version 16.2

Initially, only ROOT or MLSV built-in commands of the calculator were used —> and the answer then might take a while to appear — or even never appear at all.

Because of many "pitfalls", all nicely solved by Albert Chan in his thread LambertW, the program had to be modified, hopefully more or less correctly, thanks to and according to Albert Chan's implementations.

The resulting program, with its possible apparent lack of continuity in the structure and its redundancies, is not supposed to be elegant or always most efficient; it just works fine, above all with Android phone application EMU48, and reflects, with more or less success, its successive "improvements" according to the different situations.

Don't hesitate to compare the exactness of the results with Wolfram Alpha or with the very fast and compact program by John Keith after Albert Chan's suggestions.

Regarding the accuracy of the results
Entering the algebraic expression '-1/e' as input, you will get W0 & W-1 = exactly -1:
W0
(
'-(1/e)'~-.367879441171
)
: -1
& W-1
(
'-(1/e)'~-.367879441171
)
: -1.
But entering the approximate value of -1/e, ie the real number -.367879441171, will produce the double output ≠-1 W0
(
-.367879441171
)
: -.999997710398
& W-1
(
-.367879441171
)
: -1.00000141421.