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

%I #7 Aug 03 2021 13:38:24

%S 6,3,5,7,9,4,2,3,3,9,7,1,9,2,6,5,5,1,4,3,5,4,2,6,6,4,2,1,0,0,1,5,9,2,

%T 2,3,2,3,8,8,1,5,0,3,7,1,6,5,9,8,8,6,8,9,6,3,7,8,9,2,5,4,1,7,8,0,3,0,

%U 3,4,3,4,0,1,4,0,4,0,9,4,6,6,6,4,9,4,2,7,1,1,3,1,7,4,3,1,3,0,4,5,5,6,7,6,9,7

%N Decimal expansion of x > 0 satisfying 4*x^2 - 2*x*cos(x) = sin(x).

%C See A199597 for a guide to related sequences. The Mathematica program includes a graph.

%e 0.63579423397192655143542664210015922323...

%t a = 4; b = -2; c = 1;

%t f[x_] := a*x^2 + b*x*Cos[x]; g[x_] := c*Sin[x]

%t Plot[{f[x], g[x]}, {x, -2, 2}, {AxesOrigin -> {0, 0}}]

%t r = x /. FindRoot[f[x] == g[x], {x, .63, .64}, WorkingPrecision -> 110]

%t RealDigits[r] (* A199867 *)

%Y Cf. A199597.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Nov 11 2011

%E a(90) onwards corrected by _Georg Fischer_, Aug 03 2021