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A199460 Decimal expansion of x > 0 satisfying x = 2*sin(x). 7

%I #32 Jul 23 2021 22:02:12

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

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

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

%N Decimal expansion of x > 0 satisfying x = 2*sin(x).

%C See A199429 for a guide to related sequences. The Mathematica program includes a graph.

%C A solution to the functional equation f'(z) = f(z+1)-f(z-1) is f(z) = exp(x*i*z). - _Jean-François Alcover_, Apr 04 2014

%C The solution c of s/c = 2, where s = arclength and c = chord length on the unit circle. - _Clark Kimberling_, Jul 08 2020

%F Equals lim_{n->oo} x_n where x_(n+1)=2*sin(x_n). - _Christoph B. Kassir_, Jun 30 2021

%e 1.895494267033980947144035738093601691751...

%t a = 1; b = -2; c = 0;

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

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

%t r = x /. FindRoot[f[x] == g[x], {x, 1.89, 1.90}, WorkingPrecision -> 110]

%t RealDigits[r] (* A199460 greatest of three roots *)

%Y Cf. A199429.

%K nonn,cons

%O 1,2

%A _Clark Kimberling_, Nov 07 2011

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Last modified March 28 04:13 EDT 2024. Contains 371235 sequences. (Running on oeis4.)