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%I #6 Jun 28 2024 09:55:34
%S 4,1,6,7,7,8,2,7,9,8,0,0,4,8,2,3,4,9,2,1,8,0,8,0,7,3,5,1,1,2,1,0,9,6,
%T 7,4,5,7,0,1,9,5,8,9,6,1,1,0,1,7,4,9,9,3,9,8,4,1,2,3,7,5,6,0,3,4,2,7,
%U 8,9,1,7,5,0,5,3,1,1,8,6,2,9,9,6,3,0,6,0,9,6,2,8
%N Decimal expansion of the location of the minimum of f(x)=x*cosh(1/(2*x)) for x>0.
%C This constant separates the parameter ranges of dimensionless tension in determining the shape of the sag curve of a heavy rope into slack solution and tensioned solution.
%e 0.41677827980048234921808073511210967457019589611...
%t RealDigits[x /. FindRoot[Tanh[1/(2*x)] == 2*x, {x, 1/2}, WorkingPrecision -> 100]][[1]] (* _Vaclav Kotesovec_, Jun 28 2024 *)
%o (PARI) my(f(x)=x*cosh(1/(2*x))); solve(x=0.3,0.5,f'(x))
%Y The function value at the minimum is A240358/2 = 0.754439780769159964454942244...
%K nonn,cons
%O 0,1
%A _Hugo Pfoertner_, Jun 27 2024