A199737 Decimal expansion of least x satisfying x^2-4*x*cos(x)=sin(x).

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

Offset: 1

Author

Clark Kimberling, Nov 09 2011

Keywords

• nonn
• cons

Comments

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

Examples

			least: -3.6417365104232030891568017121916889194744...
greatest:  1.39694868354568477235286357946526821398...
		

Links

• Index entries for transcendental numbers.

Crossrefs

Cf. A199597.

Programs

Mathematica

a = 1; b = -4; c = 1;
f[x_] := a*x^2 + b*x*Cos[x]; g[x_] := c*Sin[x]
Plot[{f[x], g[x]}, {x, -4, 2}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, -3.7, -3.6}, WorkingPrecision -> 110]
RealDigits[r]   (* A199737 least root *)
r = x /. FindRoot[f[x] == g[x], {x, 1.39, 1.40}, WorkingPrecision -> 110]
RealDigits[r]   (* A199738 greatest root *)