A332330 - OEIS

A332330

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

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

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OFFSET

1,1

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 next-to-least positive zero of p(2n,x) if there is such a zero. The limit of z(n) is 3 Pi/2 = 4.7123889..., as in A197723.

LINKS

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

EXAMPLE

Next-to-least positive zero = 4.240796986376269455128706342145526...

MATHEMATICA

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