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A198883 Decimal expansion of x>0 satisfying 2*x^2-4*cos(x)=-3.

%I A198883 #10 Feb 07 2025 17:45:16
%S A198883 5,0,2,6,3,0,1,8,3,5,2,3,6,8,1,8,9,7,0,4,3,8,6,9,2,1,6,0,0,9,3,5,3,8,
%T A198883 7,5,3,1,7,9,7,6,9,8,2,3,1,6,6,8,7,8,2,3,5,4,5,9,9,1,4,4,5,8,7,2,1,4,
%U A198883 4,5,8,9,3,0,4,1,4,0,4,8,8,4,9,3,2,8,5,4,0,0,6,8,5,9,1,2,0,2,1
%N A198883 Decimal expansion of x>0 satisfying 2*x^2-4*cos(x)=-3.
%C A198883 See A198755 for a guide to related sequences. The Mathematica program includes a graph.
%H A198883 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A198883 0.5026301835236818970438692160093538753179...
%t A198883 a = 2; b = -4; c = -3;
%t A198883 f[x_] := a*x^2 + b*Cos[x]; g[x_] := c
%t A198883 Plot[{f[x], g[x]}, {x, -2, 2}, {AxesOrigin -> {0, 0}}]
%t A198883 r = x /. FindRoot[f[x] == g[x], {x, .5, .51}, WorkingPrecision -> 110]
%t A198883 RealDigits[r] (* A198883 *)
%Y A198883 Cf. A198755.
%K A198883 nonn,cons
%O A198883 0,1
%A A198883 _Clark Kimberling_, Oct 31 2011