%I #19 Apr 18 2020 03:26:28
%S 3,1,4,3,5,8,0,8,8,8,3,4,9,9,8,0,0,5,8,6,9,4,3,5,8,7,8,1,8,2,0,2,2,7,
%T 8,9,9,5,6,6,6,6,9,6,0,4,0,6,1,5,5,7,3,4,5,7,7,8,9,2,4,9,0,2,4,2,8,6,
%U 4,2,9,5,3,5,6,3,8,2,5,8,9,0,7,3,9,3
%N Decimal expansion of largest negative solution to x! = x, or Gamma(x+1)=x, negated.
%C Fixed point for Gamma(x+1) closest to 1 and 2.
%C By a mathematical coincidence, the negated expansion of the number is within 0.0633%, or 1 part in 1580 from Pi. Likewise, this constant is 1 part in 1580 away from -Pi.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/GammaFunction.html">Gamma Function</a>.
%e x = -3.1435808883499800586943587818...
%t RealDigits[x /. FindRoot[Gamma[x + 1] == x, {x, -3.1}, WorkingPrecision -> 100], 10, 100][[1]] (* _Vaclav Kotesovec_, Apr 18 2020 *)
%o (PARI) solve(x=3.1,3.2,gamma(1-x)+x) \\ _Charles R Greathouse IV_, Apr 18 2020
%K nonn,cons
%O 1,1
%A _Eliora Ben-Gurion_, Mar 27 2020