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A199000 Decimal expansion of x>0 satisfying 4*x^2-4*cos(x)=-3.

%I A199000 #8 Feb 07 2025 19:45:48
%S A199000 4,0,9,1,9,5,7,0,5,5,2,8,4,3,0,3,9,3,7,1,2,0,4,0,4,6,0,6,0,7,2,6,7,1,
%T A199000 5,0,3,8,3,1,2,8,0,4,9,4,7,8,2,9,4,7,6,4,7,6,1,7,7,7,3,1,2,6,6,8,3,1,
%U A199000 1,9,2,4,7,0,7,1,9,6,6,6,0,0,8,8,5,2,0,6,5,0,2,2,7,7,3,2,2,6,1
%N A199000 Decimal expansion of x>0 satisfying 4*x^2-4*cos(x)=-3.
%C A199000 See A198755 for a guide to related sequences. The Mathematica program includes a graph.
%H A199000 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A199000 0.40919570552843039371204046060726715038312804...
%t A199000 a = 4; b = -4; c = -3;
%t A199000 f[x_] := a*x^2 + b*Cos[x]; g[x_] := c
%t A199000 Plot[{f[x], g[x]}, {x, -2, 2}, {AxesOrigin -> {0, 0}}]
%t A199000 r = x /. FindRoot[f[x] == g[x], {x, .4, .41}, WorkingPrecision -> 110]
%t A199000 RealDigits[r] (* A199000 *)
%Y A199000 Cf. A198755.
%K A199000 nonn,cons
%O A199000 0,1
%A A199000 _Clark Kimberling_, Nov 01 2011