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.

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

Author

Eli Jaffe, Mar 27 2016

Keywords

• nonn
• cons

Examples

			-0.42131506848449048984606891964560158397494449...
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..10000
• Eric Weisstein's World of Mathematics, Lambert W-Function
• Wikipedia, Lambert W function

Programs

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 ]