cp's OEIS Frontend

A277053 Decimal expansion of real zero x between 78 and 79 of the derivative of the function plotting the invariant points for the exponential function of the form x^y = y.

%I A277053 #20 May 22 2025 04:11:55
%S A277053 7,8,5,1,7,6,6,8,8,7,3,3,8,0,6,8,5,1,9,2,8,2,9,7,5,9,9,9,0,3,9,1,9,9,
%T A277053 3,7,6,0,0,4,9,5,9,5,1,3,1,9,5,8,9,3,6,7,1,5,5,8,0,1,1,0,8,4,7,3,5,2,
%U A277053 7,1,7,3,1,2,6,0,6,7,6,3,0,0,6,4,2,6,8,9,0,6,0,7,5,1,8,8,1,6,1,7,7,8,2,3,9,7,2,2,3,9,1,7,7,4,3,0,2,7,7,7,7,5,8,2,4,0,4,0,9,3
%N A277053 Decimal expansion of real zero x between 78 and 79 of the derivative of the function plotting the invariant points for the exponential function of the form x^y = y.
%C A277053 It has not yet been determined if this number has a closed form.
%F A277053 The derivative x^y = y, or y = -ProductLog(-log(x))/log(x) when solved for y, is the function in which this value is a root. The derivative is (ProductLog(-log(x)))^2/(x*(log(x))^2*(1+ProductLog(-log(x)))).
%e A277053 78.5176688733806851928297599903919937600495951319589367155801108473527173126...
%t A277053 FindRoot[Re[ProductLog[-Log[x]]^2/(x Log[x]^2 (1 + ProductLog[-Log[x]]))], {x, 78, 79},
%t A277053 WorkingPrecision -> 261]
%Y A277053 Cf. A042972, A073229.
%K A277053 nonn,cons
%O A277053 2,1
%A A277053 _David D. Acker_, Sep 26 2016