A332329 - OEIS

%I #8 Feb 12 2020 19:47:36

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

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

%U 6,6,3,1,6,9,2,1,2,3,5,9,3,1,7,5,7,2

%N Decimal expansion of the next-to-least positive zero of the 4th Maclaurin polynomial of cos x.

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

%C 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.

%e Next-to-least positive zero = 3.0763780026417030969660258639367224

%t z = 150; p[n_, x_] := Normal[Series[Cos[x], {x, 0, n}]]

%t t = x /. NSolve[p[4, x] == 0, x, z][[4]]

%t u = RealDigits[t][[1]]

%t Plot[Evaluate[p[4, x]], {x, -1, 4}]

%Y Cf. A197723, A323326, A323330, A323331.

%K nonn,cons,easy

%O 1,1

%A _Clark Kimberling_, Feb 11 2020