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

%I #13 Feb 08 2025 22:32:51

%S 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,

%T 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,

%U 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

%N Decimal expansion of x>0 satisfying 2*x^2-x*cos(x)=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 0.797775593301396564734083229129024544418428941...

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

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

%t Plot[{f[x], g[x]}, {x, -1, 2}, {AxesOrigin -> {0, 0}}]

%t r = x /. FindRoot[f[x] == g[x], {x, .79, .80}, WorkingPrecision -> 110]

%t RealDigits[r] (* A199742 *)

%Y Cf. A199597.

%K nonn,cons,changed

%O 0,1

%A _Clark Kimberling_, Nov 10 2011

%E Name corrected by _Sean A. Irvine_, Jan 12 2025