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

%I #8 Feb 08 2025 22:37:22

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

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

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

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

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

%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.

%e 0.4646025259952393958921906007574784643540565243570...

%t a = 4; b = -1; 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, .46, .47}, WorkingPrecision -> 110]

%t RealDigits[r] (* A199865 *)

%Y Cf. A199597.

%K nonn,cons,changed

%O 0,1

%A _Clark Kimberling_, Nov 11 2011