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A332328 Decimal expansion of the least positive zero of the 8th Maclaurin polynomial of cos x. 0
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 (list; constant; graph; refs; listen; history; text; internal format)
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}]]

t = x /. NSolve[p[8, x] == 0, x, z][[5]]

u = RealDigits[t][[1]]

Plot[Evaluate[p[8, x]], {x, -1, 2}]

CROSSREFS

Cf. A019669, A332326.

Sequence in context: A085679 A019669 A088394 * A021950 A072417 A133412

Adjacent sequences:  A332325 A332326 A332327 * A332329 A332330 A332331

KEYWORD

nonn,cons,easy

AUTHOR

Clark Kimberling, Feb 11 2020

STATUS

approved

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Last modified November 27 16:35 EST 2021. Contains 349394 sequences. (Running on oeis4.)