OFFSET
1,2
COMMENTS
LINKS
R. Witula, D. Slota and Szeged Problem Group "Fejentalaltuka", An Iteration Convergence: 11318[2007, 745], Amer. Math. Monthly, 116 No 7 (2009), 648-649.
EXAMPLE
We have x(3) = 1.4127945857276222... < sqrt(2).
MATHEMATICA
f[x_] := Cos[x] - Sin[x];
FindRoot[f[f[x]] - x, {x, 1.4}, WorkingPrecision -> 110] (* T. D. Noe, Sep 24 2012; first line by Rick L. Shepherd, Jan 04 2014 *)
PROG
(PARI)
default(realprecision, 110);
f(x) = cos(x) - sin(x);
solve(x = 1.4, 1.5, f(f(x)) - x) \\ Rick L. Shepherd, Jan 03 2014
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Roman Witula, Sep 18 2012
EXTENSIONS
Offset corrected by Rick L. Shepherd, Jan 03 2014
STATUS
approved