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A332327
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Decimal expansion of the least positive zero of the 6th Maclaurin polynomial of cos x.
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1
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1, 5, 6, 9, 9, 0, 5, 8, 2, 5, 1, 6, 1, 1, 9, 1, 4, 5, 6, 6, 1, 8, 1, 2, 2, 1, 8, 5, 7, 8, 1, 8, 2, 9, 7, 4, 8, 3, 7, 2, 4, 5, 2, 3, 2, 5, 4, 9, 7, 3, 1, 6, 8, 3, 7, 1, 2, 4, 8, 9, 5, 4, 6, 9, 2, 0, 0, 6, 3, 4, 4, 5, 3, 2, 4, 4, 6, 5, 2, 7, 2, 8, 2, 5, 6, 2
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OFFSET
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1,2
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COMMENTS
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The Maclaurin polynomial p(2n,x) of cos x is 1 - x^2/2! + x^4/4! + ... + (-1)^n x^(2n)/(2n)!.
Let z(n) be the least positive zero of p(2n,x). The limit of z(n) is Pi/2 = 1.570796326..., as in A019669.
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LINKS
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EXAMPLE
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Least positive zero = 1.56990582516119145661812218578182974...
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MATHEMATICA
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z = 150; p[n_, x_] := Normal[Series[Cos[x], {x, 0, n}]]
t = x /. NSolve[p[6, x] == 0, x, z][[4]]
u = RealDigits[t][[1]]
Plot[Evaluate[p[6, x]], {x, -1, 2}]
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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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