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

2

`%I #5 Mar 30 2012 18:57:58
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`%S 9,5,4,9,5,6,8,5,5,8,6,2,7,9,1,4,3,4,7,2,5,7,1,4,1,1,1,6,0,9,9,5,6,1,
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`%T 5,7,9,6,4,9,1,2,2,5,0,6,0,6,8,6,8,6,0,5,7,5,9,6,8,5,7,5,2,9,0,3,4,9,
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`%U 7,4,5,9,0,1,2,0,6,4,9,1,6,2,6,2,7,1,6,3,6,5,7,7,8,1,2,8,5,4,2
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`%N Decimal expansion of x>0 satisfying 3*x^2-2*x*cos(x)=2*sin(x).
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`%C See A199597 for a guide to related sequences. The Mathematica program includes a graph.
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`%e x=0.9549568558627914347257141116099561579649122...
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`%t a = 3; b = -2; c = 2;
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`%t f[x_] := a*x^2 + b*x*Cos[x]; g[x_] := c*Sin[x]
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`%t Plot[{f[x], g[x]}, {x, -1, 2}, {AxesOrigin -> {0, 0}}]
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`%t r = x /. FindRoot[f[x] == g[x], {x, .95, .96}, WorkingPrecision -> 110]
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`%t RealDigits[r] (* A199792 *)
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`%Y Cf. A199597.
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`%K nonn,cons
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`%O 0,1
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`%A _Clark Kimberling_, Nov 10 2011
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