A364931 - OEIS

%I #10 Sep 15 2023 04:29:33

%S 6,5,9,0,4,6,0,6,8,4,0,7,4,0,6,6,6,0,9,8,4,3,8,6,4,9,5,9,2,8,8,6,7,5,

%T 5,1,6,9,8,0,9,0,3,3,0,3,5,7,1,1,5,1,8,8,4,8,9,2,9,4,6,3,0,8,0,4,2,2,

%U 4,1,1,3,0,4,2,4,2,9,7,5,7,5,7,9,0,3,4,7,3,5,6,4,8,2,8,2,0,1,0,5

%N Decimal expansion of the solution to 1 / (1 + e^(-x)) = x.

%C Fixed point of sigmoid (standard logistic function) as well as its inverse (logit).

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/SigmoidFunction.html">Sigmoid Function</a>.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Logistic_function">Logistic Function</a>.

%e 0.6590460684074066...

%p Digits:=100: fsolve(1/(1+exp(-x))-x, x);

%t RealDigits[FindRoot[1/(1+Exp[-x])-x, {x, 0.6}, WorkingPrecision -> 100][[1, 2]], 10, 100][[1]]

%o (PARI) default(realprecision, 100); solve(x=0.4,0.7,1/(1+exp(-x))-x)

%K nonn,cons

%O 0,1

%A _Michal Paulovic_, Aug 13 2023