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Decimal expansion of largest negative solution to x! = x, or Gamma(x+1)=x, negated.
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%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