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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.

%I A271310 #16 Feb 16 2025 08:33:33
%S A271310 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 A271310 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 A271310 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 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.
%H A271310 G. C. Greubel, <a href="/A271310/b271310.txt">Table of n, a(n) for n = 0..10000</a>
%H A271310 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>
%H A271310 Wikipedia, <a href="http://en.wikipedia.org/wiki/Lambert_W_function">Lambert W function</a>
%e A271310 -0.42131506848449048984606891964560158397494449...
%p A271310 f:= z-> Re(LambertW(-z)/ln(-z))-Im(LambertW(-z)/ln(-z)):
%p A271310 Digits:= 200:
%p A271310 fsolve(f(x), x=0.4..1.0);  # _Alois P. Heinz_, May 04 2016
%t A271310 FindRoot[Im[ProductLog[z]/Log[z]] - Re[ProductLog[z]/Log[z]] == 0, {z, -0.42241, -0.416207}, WorkingPrecision ->100 ]
%K A271310 nonn,cons
%O A271310 0,1
%A A271310 _Eli Jaffe_, Mar 27 2016