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A277069 Decimal expansion of the real part of the root of the function x^y = y. 1

%I

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

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

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

%N Decimal expansion of the real part of the root of the function x^y = y.

%C This value is negative.

%C It is not known if this number has a closed form.

%C This root occurs on the real component of the function x^y = y for x values which are all real.

%F Original fixed point function is of the form: x^y = y. When solved for y: y = -ProductLog(-log(x))/log(x).

%e -99.1120147991877404695252398904774418725997764195131575672373129...

%t FindRoot[Re[-ProductLog[-Log[x]]/Log[x]], {x, -100, -99}, WorkingPrecision -> 261]

%Y Cf. A277067.

%K nonn,cons

%O 2,1

%A _David D. Acker_, Sep 27 2016

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Last modified May 19 13:24 EDT 2022. Contains 353833 sequences. (Running on oeis4.)