A199607 - OEIS

%I #8 Feb 08 2025 10:08:47

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

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

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

%N Decimal expansion of least x satisfying x^2+3*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 least: -0.5973392503648539750049736135997669028331...

%e greatest:  3.0481385953651166891446050593739052208...

%t a = 1; b = 3; c = 2;

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

%t Plot[{f[x], g[x]}, {x, -2, 4}, {AxesOrigin -> {0, 0}}]

%t r = x /. FindRoot[f[x] == g[x], {x, -.6, -.5}, WorkingPrecision -> 110]

%t RealDigits[r]  (* A199607, least of 4 roots *)

%t r = x /. FindRoot[f[x] == g[x], {x, 3, 3.1}, WorkingPrecision -> 110]

%t RealDigits[r]  (* A199708, greatest of 4 roots *)

%Y Cf. A199597.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Nov 08 2011