A199619 Decimal expansion of least x>0 satisfying x^2+4*x*cos(x)=4*sin(x).

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

Offset: 0

Author

Clark Kimberling, Nov 08 2011

Keywords

• nonn
• cons

Comments

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

Examples

			least: 0.80005334262741575936859027990893321963...
greatest:  3.4528998885329277803363008378649838...
		

Links

• Index entries for transcendental numbers.

Crossrefs

Cf. A199597.

Programs

Mathematica

a = 1; b = 4; c = 4;
f[x_] := a*x^2 + b*x*Cos[x]; g[x_] := c*Sin[x]
Plot[{f[x], g[x]}, {x, -.5, 4}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, .8, .81}, WorkingPrecision -> 110]
RealDigits[r]  (* A199619, least pos root *)
r = x /. FindRoot[f[x] == g[x], {x, 3.4, 3.5}, WorkingPrecision -> 110]
RealDigits[r]  (* A199620, greatest of 3 roots *)