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A199797 Decimal expansion of x>0 satisfying 3*x^2-x*cos(x)=sin(x).

%I A199797 #8 Feb 08 2025 22:36:25
%S A199797 5,9,1,0,4,7,6,6,8,0,7,2,5,4,9,5,8,7,3,9,7,8,0,9,8,4,5,4,6,4,2,1,2,4,
%T A199797 7,3,0,5,1,6,9,0,1,3,6,4,2,8,0,1,9,8,6,6,1,9,8,3,5,2,5,6,0,1,2,6,2,6,
%U A199797 2,3,5,7,9,0,3,0,4,5,0,7,2,7,3,2,0,7,5,4,2,5,6,1,5,9,2,7,3,4,8
%N A199797 Decimal expansion of x>0 satisfying 3*x^2-x*cos(x)=sin(x).
%C A199797 See A199597 for a guide to related sequences. The Mathematica program includes a graph.
%H A199797 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A199797 0.5910476680725495873978098454642124730516901364280...
%t A199797 a = 3; b = -1; c = 1;
%t A199797 f[x_] := a*x^2 + b*x*Cos[x]; g[x_] := c*Sin[x]
%t A199797 Plot[{f[x], g[x]}, {x, -2, 2}, {AxesOrigin -> {0, 0}}]
%t A199797 r = x /. FindRoot[f[x] == g[x], {x, .59, .60}, WorkingPrecision -> 110]
%t A199797 RealDigits[r]    (* A199797 *)
%Y A199797 Cf. A199597.
%K A199797 nonn,cons
%O A199797 0,1
%A A199797 _Clark Kimberling_, Nov 10 2011