A373918 Decimal expansion of the location of the minimum of f(x)=x*cosh(1/(2*x)) for x>0.

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, 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, 8, 9, 1, 7, 5, 0, 5, 3, 1, 1, 8, 6, 2, 9, 9, 6, 3, 0, 6, 0, 9, 6, 2, 8

Offset: 0

Author

Hugo Pfoertner, Jun 27 2024

Keywords

• nonn
• cons

Comments

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.

Examples

			0.41677827980048234921808073511210967457019589611...
		

Crossrefs

The function value at the minimum is A240358/2 = 0.754439780769159964454942244...

Programs

Mathematica

RealDigits[x /. FindRoot[Tanh[1/(2*x)] == 2*x, {x, 1/2}, WorkingPrecision -> 100]][[1]] (* Vaclav Kotesovec, Jun 28 2024 *)

PARI

my(f(x)=x*cosh(1/(2*x))); solve(x=0.3,0.5,f'(x))