A332328 - OEIS

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A332328

Decimal expansion of the least positive zero of the 8th Maclaurin polynomial of cos x.

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

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OFFSET

1,2

COMMENTS

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.

LINKS

Table of n, a(n) for n=1..86.

EXAMPLE

Least positive zero = 1.5708210679533907291728211531492495531616658...

MATHEMATICA

z = 150; p[n_, x_] := Normal[Series[Cos[x], {x, 0, n}]]