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Decimal expansion of least x>0 satisfying 2-x^2=tan(x).
2

%I #7 Jan 30 2025 13:42:14

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

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

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

%N Decimal expansion of least x>0 satisfying 2-x^2=tan(x).

%C See A200614 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 0.8837599572083158645319472890521286286971...

%t a = -1; c = 2;

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

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

%t r = x /. FindRoot[f[x] == g[x], {x, .8, .9}, WorkingPrecision -> 110]

%t RealDigits[r] (* A200686 *)

%Y Cf. A200338.

%K nonn,cons,changed

%O 0,1

%A _Clark Kimberling_, Nov 20 2011