A333477 Decimal expansion of largest negative solution to x! = x, or Gamma(x+1)=x, negated.

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

Offset: 1

Author

Eliora Ben-Gurion, Mar 27 2020

Keywords

• nonn
• cons

Comments

Fixed point for Gamma(x+1) closest to 1 and 2.

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.

Examples

			x = -3.1435808883499800586943587818...
		

Links

• Eric Weisstein's World of Mathematics, Gamma Function.

Programs

Mathematica

RealDigits[x /. FindRoot[Gamma[x + 1] == x, {x, -3.1}, WorkingPrecision -> 100], 10, 100][[1]] (* Vaclav Kotesovec, Apr 18 2020 *)

PARI

solve(x=3.1,3.2,gamma(1-x)+x) \\ Charles R Greathouse IV, Apr 18 2020