A332328 Decimal expansion of the least positive zero of the 8th Maclaurin polynomial of cos x.

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

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 least positive zero of p(2n,x). The limit of z(n) is Pi/2 = 1.570796326..., as in A019669.

Examples

			Least positive zero = 1.5708210679533907291728211531492495531616658...
		

Crossrefs

Cf. A019669, A332326.

Programs

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}]