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A271310
Decimal expansion of the leftmost root of Im(W(z)/log(z)) = Re(W(z)/log(z)) (negated), where W(z) denotes the Lambert W function.
1
4, 2, 1, 3, 1, 5, 0, 6, 8, 4, 8, 4, 4, 9, 0, 4, 8, 9, 8, 4, 6, 0, 6, 8, 9, 1, 9, 6, 4, 5, 6, 0, 1, 5, 8, 3, 9, 7, 4, 9, 4, 4, 4, 9, 0, 1, 7, 6, 6, 0, 8, 0, 2, 3, 2, 4, 7, 0, 4, 2, 2, 7, 4, 9, 6, 8, 9, 2, 0, 2, 4, 2, 1, 3, 2, 5, 2, 1, 7, 4, 3, 3, 9, 2, 3, 3, 9, 4, 4, 3, 6, 1, 8, 0, 0, 0, 9, 8, 2, 4, 0, 4, 8, 1, 7
OFFSET
0,1
LINKS
Eric Weisstein's World of Mathematics, Lambert W-Function
EXAMPLE
-0.42131506848449048984606891964560158397494449...
MAPLE
f:= z-> Re(LambertW(-z)/ln(-z))-Im(LambertW(-z)/ln(-z)):
Digits:= 200:
fsolve(f(x), x=0.4..1.0); # Alois P. Heinz, May 04 2016
MATHEMATICA
FindRoot[Im[ProductLog[z]/Log[z]] - Re[ProductLog[z]/Log[z]] == 0, {z, -0.42241, -0.416207}, WorkingPrecision ->100 ]
CROSSREFS
Sequence in context: A097525 A309975 A010124 * A071406 A337063 A375119
KEYWORD
nonn,cons
AUTHOR
Eli Jaffe, Mar 27 2016
STATUS
approved