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

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

Author

Clark Kimberling, Feb 11 2020

Keywords

• nonn
• cons
• easy

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.

Examples

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

Crossrefs

Cf. A197723, A332329, A332330.

Programs

Mathematica

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}]