ea9b5437-ba6c-4efb-856c-411df84999a8 16 4 5 decimal

&[DATE] &[TIME] - &[FILENAME]

http://mathworld.wolfram.com/LambertW-Function.html http://www.jfepperson.org/2edition-web/lambert.pdf

Lambert W principal branch

x W0 w w exp * x - 0 ≡ w 1 e / - roots : x W1 w w exp * x - 0 ≡ w 2 sqrt - roots : 21 line

x ProductLog 15 decimals u x e > x ln x ln ln - x 1 e / + sqrt 1 e / sqrt - if 11 line : w 2 u * : u w - abs u abs / 1010 -^> w u : u u 2^x e u -^* + 1 u + / eval : 21 line while u 51 line :

1 e / - 1010 -^+ W0 1 e / - ProductLog 21 mat 0.999976684 - 0.999999979 - 21 mat

e W0 e ProductLog 21 mat 1.000000000000000 1.000000000000000 21 mat

1 W0 1 ProductLog 21 mat 0.567143290409783 0.567143290409783 21 mat

is approximalety 0.5671432904097838729999686622 [Neil Sloane] Ω 1 W ≡

Plot eval(,,) Lambert W(x)

x ProductLog

Lambert [root conventional]

x W0 x W1 1 e / - 1 1 e / - 5 - 2 2 mat 3 1 sys