OFFSET
0,1
COMMENTS
Other fixed points (mod 1) are 0, 1/2 and 1-A048819. - Joseph Biberstine (jrbibers(AT)indiana.edu), Jun 10 2006
REFERENCES
S. R. Finch, Mathematical Constants, Cambridge, 2003, Section 6.9 Minkowski-Bower constant, pp. 441-443.
LINKS
Jean-François Alcover, Graph of the question mark function.
Steven R. Finch, Minkowski's Question Mark Function [Broken link]
Steven R. Finch, Minkowski's Question Mark Function [From the Wayback machine]
Eric Weisstein's World of Mathematics, Minkowski-Bower Constant
Eric Weisstein's World of Mathematics, Minkowski's Question Mark Function
EXAMPLE
0.4203723394232230756409930066462218739491898666...
MATHEMATICA
digits = 99; n0 = 3; dx = 10^-n0; qm[x_] := (ac = Accumulate[ContinuedFraction[x, 200]]; 2 + 2*Sum[(-1)^n* 2^(-ac[[n]]), {n, 1, Length[ac]}]); x = dx; While[N[qm[x], digits+5] < x, x = x + dx]; x0 = x - dx; Do[dx = 10^-n; x = x0; While[N[qm[x], digits+5] < x, x = N[x + dx, digits+5]]; x0 = x - dx , {n, n0+1, digits}]; RealDigits[x0, 10, digits] // First (* Jean-François Alcover, Oct 13 2014 *)
RealDigits[x /. FindRoot[MinkowskiQuestionMark[x] - x, {x, .42, .421}, WorkingPrecision -> 200, MaxIterations -> 500], 10, 99][[1]] (* Eric W. Weisstein, Jan 06 2023 *)
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Christian G. Bower, Apr 15 1999
STATUS
approved