A332329 -id:A332329 - cp's OEIS frontend

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

Clark Kimberling, Feb 11 2020

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.

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

Cf. A197723, A332330, A332329.

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}]

A332331 Decimal expansion of the next-to-least positive zero of the 12th Maclaurin polynomial of cos x.

Original entry on oeis.org

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

Offset: 1

Clark Kimberling, Feb 11 2020

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.

			Next-to-least positive zero = 4.6865176637957574465700489837907750...

Cf. A197723, A332329, A332330.

z = 150; p[n_, x_] := Normal[Series[Cos[x], {x, 0, n}]]
t = x /. NSolve[p[12, x] == 0, x, z][[8]]
u = RealDigits[t][[1]]
Plot[Evaluate[p[12, x]], {x, -1, 5}]

cp's OEIS Frontend

A332330 Decimal expansion of the next-to-least positive zero of the 8th Maclaurin polynomial of cos x.

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