A332326 Decimal expansion of the least positive zero of the 4th Maclaurin polynomial of cos x.

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

Offset

1,2

Comments

The Maclaurin polynomial p(2n,x) of cos x is 1 - x^2/2! + x^4/4! + ... + (-1)^n ^(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 = 1.592450434036251381668998670484001969...

Mathematica

z = 150; p[n_, x_] := Normal[Series[Cos[x], {x, 0, n}]]
t = x /. NSolve[p[4, x] == 0, x, z][[3]]
u = RealDigits[t][[1]]
Plot[Evaluate[p[4, x]], {x, -1, 4}]

Crossrefs

Cf. A019669, A332325, A332327, A323328, A323329.

Sequence in context: A248191 A323985 A198734 * A200009 A303662 A011494

Adjacent sequences: A332323 A332324 A332325 * A332327 A332328 A332329

Keyword

nonn,cons,easy

Author

Clark Kimberling, Feb 11 2020

Status

approved