A199721 - OEIS

%I #8 Feb 08 2025 22:27:04

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

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

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

%N Decimal expansion of x>0 satisfying x^2-x*cos(x)=2*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 1.46433510386806766962372047842040837624925...

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

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

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

%t r = x /. FindRoot[f[x] == g[x], {x, 1.4, 1.5}, WorkingPrecision -> 110]

%t RealDigits[r]  (* A199721 *)

%Y Cf. A199597.

%K nonn,cons,changed

%O 1,2

%A _Clark Kimberling_, Nov 09 2011