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A201670
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Decimal expansion of least x satisfying 5*x^2 - 1 = csc(x) and 0<x<Pi.
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3
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7, 1, 1, 5, 3, 3, 8, 8, 8, 3, 6, 7, 1, 5, 1, 4, 9, 9, 2, 4, 6, 7, 9, 6, 3, 0, 7, 4, 2, 8, 2, 1, 2, 5, 5, 6, 7, 7, 2, 7, 9, 9, 2, 0, 5, 9, 3, 7, 5, 3, 9, 0, 7, 5, 8, 0, 6, 0, 8, 8, 5, 4, 9, 8, 9, 2, 8, 4, 1, 5, 5, 0, 8, 2, 3, 4, 4, 8, 5, 4, 3, 7, 4, 6, 3, 2, 1, 8, 4, 5, 9, 7, 9, 8, 6, 8, 3, 4, 3
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OFFSET
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0,1
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COMMENTS
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See A201564 for a guide to related sequences. The Mathematica program includes a graph.
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LINKS
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EXAMPLE
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least: 0.711533888367151499246796307428212556772...
greatest: 3.120622993086918805141273424623066002...
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MATHEMATICA
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a = 5; c = -1;
f[x_] := a*x^2 + c; g[x_] := Csc[x]
Plot[{f[x], g[x]}, {x, 0, Pi}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, .7, .8}, WorkingPrecision -> 110]
r = x /. FindRoot[f[x] == g[x], {x, 3.0, 3.14}, WorkingPrecision -> 110]
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PROG
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(PARI) a=5; c=-1; solve(x=0.5, 1, a*x^2 + c - 1/sin(x)) \\ G. C. Greubel, Sep 11 2018
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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