A199742 Decimal expansion of x>0 satisfying 2*x^2-x*cos(x)=sin(x).

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

Offset: 0

Author

Clark Kimberling, Nov 10 2011

Keywords

• nonn
• cons

Comments

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

Examples

			0.797775593301396564734083229129024544418428941...
		

Links

• Index entries for transcendental numbers.

Crossrefs

Cf. A199597.

Programs

Mathematica

a = 2; b = -1; c = 1;
f[x_] := a*x^2 + b*x*Cos[x]; g[x_] := c*Sin[x]
Plot[{f[x], g[x]}, {x, -1, 2}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, .79, .80}, WorkingPrecision -> 110]
RealDigits[r]   (* A199742 *)

Extensions

Name corrected by Sean A. Irvine, Jan 12 2025