A199776 - OEIS

%I #8 Feb 08 2025 22:32:46

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

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

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

%N Decimal expansion of x>0 satisfying 2*x^2-2*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 0.98037684190956145171171788026939630337700...

%t a = 2; 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, -1, 2}, {AxesOrigin -> {0, 0}}]

%t r = x /. FindRoot[f[x] == g[x], {x, .98, .99}, WorkingPrecision -> 110]

%t RealDigits[r]   (* A199776 *)

%Y Cf. A199597.

%K nonn,cons,changed

%O 0,1

%A _Clark Kimberling_, Nov 10 2011