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A173201
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Iteration x := x - (sin(x) - cos(x)*x - Pi/2)/(sin(x)*x).
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3
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1, 9, 0, 5, 6, 9, 5, 7, 2, 9, 3, 0, 9, 8, 8, 3, 8, 9, 4, 8, 8, 2, 6, 6, 6, 4, 3, 7, 1, 6, 0, 9, 6, 6, 7, 0, 3, 4, 9, 5, 0, 4, 3, 1, 2, 1, 6, 1, 2, 8, 0, 3, 2, 1, 2, 1, 9, 3, 5, 6, 4, 5, 5, 9, 9, 9, 4, 5, 4, 4, 2, 4, 0, 9, 9, 5, 7, 9, 5, 0, 2, 2, 7, 5, 7, 1, 6, 1, 6, 6, 3, 4, 6, 4, 6, 3, 0, 3, 9, 7, 1, 5, 3, 9, 8
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OFFSET
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1,2
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COMMENTS
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Decimal expansion of psi, the unique solution on (0,Pi) of sin(psi) - psi*cos(psi) = Pi/2, an auxiliary constant used in the Hall-Tenenbaum inequality applied to real multiplicative functions. - Jean-François Alcover, Sep 05 2014
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LINKS
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FORMULA
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x := x - (sin(x) - cos(x)*x - Pi/2)/(sin(x)*x).
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EXAMPLE
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A133731 = cos(1.9056957293.../2)*2.
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MATHEMATICA
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psi = x /. FindRoot[Sin[x] - x*Cos[x] == Pi/2, {x, 2}, WorkingPrecision -> 102]; RealDigits[psi] // First (* Jean-François Alcover, Sep 05 2014 *)
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PROG
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(Other) Gerd Lamprecht Iterationsrechner: #(sin(x)-cos(x)*x-PI/2)/(sin(x)*x)@Na=2; @Nb=a; a=a-Fx(a); @N@Aa-b)%3C%204e-16@N0@N1@Nc=cos(a/2)*2;
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CROSSREFS
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KEYWORD
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AUTHOR
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Gerd Lamprecht (gerdlamprecht(AT)googlemail.com), Feb 12 2010
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STATUS
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approved
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