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

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}]]
t = x /. NSolve[p[8, x] == 0, x, z][[6]]
u = RealDigits[t][[1]]
Plot[Evaluate[p[8, x]], {x, -1, 5}]

Crossrefs

Cf. A197723, A332330, A332329.

Sequence in context: A117238 A197291 A112983 * A068454 A090976 A156199

Adjacent sequences: A332327 A332328 A332329 * A332331 A332332 A332333

Keyword

nonn,cons,easy

Author

Clark Kimberling, Feb 11 2020

Status

approved