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%I #10 Sep 15 2023 04:29:53
%S 6,5,2,9,1,8,6,4,0,4,1,9,2,0,4,7,1,5,5,3,5,0,8,0,7,6,7,3,5,3,1,9,6,3,
%T 6,9,9,2,0,1,1,6,8,8,1,1,0,2,9,9,7,7,3,0,6,2,4,9,2,1,4,9,4,0,7,5,0,4,
%U 7,2,7,6,1,9,8,0,3,8,9,2,5,5,1,1,8,2,2,5,7,1,6,0,6,8,0,5,5,9,6,8,6,8,8,8,5
%N Decimal expansion of the solution to exp(-x^2) = x.
%C Fixed point of Gaussian function.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/GaussianFunction.html">Gaussian Function</a>.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Gaussian_function">Gaussian function</a>.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Lambert_W">Lambert W function</a>.
%F Equals sqrt(LambertW(2)/2).
%F Equals sqrt(A196515/2).
%F Equals sqrt(A202498).
%F Equals sqrt(A299624)/2.
%e 0.6529186404192047...
%p Digits:=105: evalf(sqrt(LambertW(2)/2));
%t RealDigits[Sqrt[ProductLog[2]/2], 10, 105][[1]]
%o (PARI) default(realprecision, 105); sqrt(lambertw(2)/2)
%Y Cf. A196515, A202498, A299624.
%K nonn,cons
%O 0,1
%A _Michal Paulovic_, Aug 14 2023
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