|
|
A373918
|
|
Decimal expansion of the location of the minimum of f(x)=x*cosh(1/(2*x)) for x>0.
|
|
1
|
|
|
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
(list;
constant;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,1
|
|
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.
|
|
LINKS
|
|
|
EXAMPLE
|
0.41677827980048234921808073511210967457019589611...
|
|
MATHEMATICA
|
RealDigits[x /. FindRoot[Tanh[1/(2*x)] == 2*x, {x, 1/2}, WorkingPrecision -> 100]][[1]] (* Vaclav Kotesovec, Jun 28 2024 *)
|
|
PROG
|
(PARI) my(f(x)=x*cosh(1/(2*x))); solve(x=0.3, 0.5, f'(x))
|
|
CROSSREFS
|
The function value at the minimum is A240358/2 = 0.754439780769159964454942244...
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|