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A198871 Decimal expansion of x>0 satisfying 2*x^2-cos(x)=1.

%I A198871 #10 Feb 07 2025 16:44:05
%S A198871 9,0,0,3,6,7,2,2,2,5,8,9,7,4,7,1,4,6,0,7,3,0,7,7,3,9,3,5,2,5,3,6,3,6,
%T A198871 5,4,6,4,0,2,7,3,0,0,3,4,4,6,1,1,0,8,6,8,0,3,0,1,1,6,9,8,2,7,2,7,2,8,
%U A198871 3,1,3,3,9,7,0,4,4,6,7,5,9,0,9,4,8,2,8,2,6,6,1,3,9,8,4,6,3,2,4
%N A198871 Decimal expansion of x>0 satisfying 2*x^2-cos(x)=1.
%C A198871 See A198755 for a guide to related sequences. The Mathematica program includes a graph.
%H A198871 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A198871 0.90036722258974714607307739352536365464027300...
%t A198871 a = 2; b = -1; c = 1;
%t A198871 f[x_] := a*x^2 + b*Cos[x]; g[x_] := c
%t A198871 Plot[{f[x], g[x]}, {x, -2, 2}, {AxesOrigin -> {0, 0}}]
%t A198871 r = x /. FindRoot[f[x] == g[x], {x, .9, .91}, WorkingPrecision -> 110]
%t A198871 RealDigits[r] (* A198871 *)
%Y A198871 Cf. A198755.
%K A198871 nonn,cons
%O A198871 0,1
%A A198871 _Clark Kimberling_, Oct 31 2011