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A199003 Decimal expansion of x>0 satisfying 4*x^2-4*cos(x)=3.

%I A199003 #8 Feb 07 2025 19:48:04
%S A199003 1,0,9,7,9,2,6,6,5,0,3,7,1,5,9,9,4,3,3,1,4,4,0,9,4,9,0,9,6,7,1,0,9,6,
%T A199003 7,0,6,9,2,0,4,4,3,7,2,4,4,0,9,0,8,1,0,1,7,7,9,1,4,0,8,7,2,1,9,3,0,5,
%U A199003 6,0,4,1,7,7,1,5,3,4,2,7,2,3,3,7,2,1,9,3,9,7,7,5,4,4,7,4,2,1,1
%N A199003 Decimal expansion of x>0 satisfying 4*x^2-4*cos(x)=3.
%C A199003 See A198755 for a guide to related sequences. The Mathematica program includes a graph.
%H A199003 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A199003 1.0979266503715994331440949096710967069204437...
%t A199003 a = 4; b = -4; c = 3;
%t A199003 f[x_] := a*x^2 + b*Cos[x]; g[x_] := c
%t A199003 Plot[{f[x], g[x]}, {x, -2, 2}, {AxesOrigin -> {0, 0}}]
%t A199003 r = x /. FindRoot[f[x] == g[x], {x, 1, 1.1}, WorkingPrecision -> 110]
%t A199003 RealDigits[r] (* A199003 *)
%Y A199003 Cf. A198755.
%K A199003 nonn,cons
%O A199003 1,3
%A A199003 _Clark Kimberling_, Nov 01 2011