A332329 Decimal expansion of the next-to-least positive zero of the 4th Maclaurin polynomial of cos x.

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

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 = 3.0763780026417030969660258639367224

Mathematica

z = 150; p[n_, x_] := Normal[Series[Cos[x], {x, 0, n}]]
t = x /. NSolve[p[4, x] == 0, x, z][[4]]
u = RealDigits[t][[1]]
Plot[Evaluate[p[4, x]], {x, -1, 4}]

Crossrefs

Cf. A197723, A323326, A323330, A323331.

Sequence in context: A298097 A155831 A106401 * A011200 A201573 A021329

Adjacent sequences: A332326 A332327 A332328 * A332330 A332331 A332332

Keyword

nonn,cons,easy

Author

Clark Kimberling, Feb 11 2020

Status

approved