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

%I #12 Feb 08 2025 09:35:23

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

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

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

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

%C See A199429 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 1.2204684659112995886828143122112448298751...

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

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

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

%t r = x /. FindRoot[f[x] == g[x], {x, 1.22, 1.23}, WorkingPrecision -> 110]

%t RealDigits[r] (* A199454 *)

%Y Cf. A199429.

%K nonn,cons,changed

%O 1,2

%A _Clark Kimberling_, Nov 06 2011