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Decimal expansion of x satisfying 3*x^2- - 1= = cot(x) and 0< < x<pi < Pi.

See A201280 for a guide to related sequences. . The Mathematica program includes a graph.

approved

editing

_Clark Kimberling (ck6(AT)evansville.edu), _, Nov 30 2011

OEIS Server: https://oeis.org/edit/global/285

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allocatedDecimal expansion of x forsatisfying Clark3*x^2-1=cot(x) and Kimberling0<x<pi.

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

0,1

See A201280 for a guide to related sequences. The Mathematica program includes a graph.

x=0.807585281442201993926581679537240754...

a = 3; c = -1;

f[x_] := a*x^2 + c; g[x_] := Cot[x]

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

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

RealDigits[r] (* A201321 *)

Cf. A201280.

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nonn,cons

Clark Kimberling (ck6(AT)evansville.edu), Nov 30 2011

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allocated for Clark Kimberling

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