%I #16 Feb 16 2025 08:33:33

%S 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,

%T 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,

%U 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

%N 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.

%H G. C. Greubel, <a href="/A271310/b271310.txt">Table of n, a(n) for n = 0..10000</a>

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Lambert_W_function">Lambert W function</a>

%e -0.42131506848449048984606891964560158397494449...

%p f:= z-> Re(LambertW(-z)/ln(-z))-Im(LambertW(-z)/ln(-z)):

%p Digits:= 200:

%p fsolve(f(x), x=0.4..1.0); # _Alois P. Heinz_, May 04 2016

%t FindRoot[Im[ProductLog[z]/Log[z]] - Re[ProductLog[z]/Log[z]] == 0, {z, -0.42241, -0.416207}, WorkingPrecision ->100 ]

%K nonn,cons,changed

%O 0,1

%A _Eli Jaffe_, Mar 27 2016