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A199002 Decimal expansion of x>0 satisfying 4*x^2-4*cos(x)=1. 2

%I #5 Mar 30 2012 18:57:56

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

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

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

%N Decimal expansion of x>0 satisfying 4*x^2-4*cos(x)=1.

%C See A198755 for a guide to related sequences. The Mathematica program includes a graph.

%e x=0.9235679051878945418585929739784101638990486411777...

%t a = 4; b = -4; c = 1;

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

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

%t r = x /. FindRoot[f[x] == g[x], {x, .92, .93}, WorkingPrecision -> 110]

%t RealDigits[r] (* A199002 *)

%Y Cf. A198755.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Nov 01 2011

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