069472e9-72f3-4b66-8789-e73d711c3c12 6 6 9 decimal

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Lambert W, principal branch

Lambert W is not a function: it is a "solution function". Don't scratch your head looking for it, you won't find. In other words: it is not a built-in aprroximation. You can fake a built-in like here in Smath. There is the good approximation "ProductLog" from Mathsoft Collaboratory.

<= solve ..... Compare Lambert ..... => roots

y W x x exp * y - 0 ≡ x 1 e / - e solve :

x Lambert w w exp * x - 0 ≡ w 0 roots :

Lambert W [solve conventional]

x W 1 e / - 1 1 e / - 1 - 2 2 mat 2 1 sys

Lambert [roots conventional]

x Lambert 1 e / - 1 1 e / - 1 - 2 2 mat 2 1 sys

ε 0.125 :

1 e / - ε + W 0.341872 -

2 W 0.852605500227717

ε 10 10.5 -^:

2 Lambert 0.852605502013724

1 e / - ε + Lambert 0.999987 -

1 Lambert 0.567143290409783

1 W 0.567143289179478

W1 Neil_Sloane (0.5671432904097838729999686622 ≡