cp's OEIS Frontend

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

%I A332330 #8 Feb 12 2020 19:48:10
%S A332330 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,
%T A332330 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,
%U A332330 1,9,4,6,1,3,0,3,3,2,7,7,6,8,8,4,5,9
%N A332330 Decimal expansion of the next-to-least positive zero of the 8th Maclaurin polynomial of cos x.
%C A332330 The Maclaurin polynomial p(2n,x) of cos x is 1 - x^2/2! + x^4/4! + ... + (-1)^n x^(2n)/(2n)!.
%C A332330 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 A332330 Next-to-least positive zero = 4.240796986376269455128706342145526...
%t A332330 z = 150; p[n_, x_] := Normal[Series[Cos[x], {x, 0, n}]]
%t A332330 t = x /. NSolve[p[8, x] == 0, x, z][[6]]
%t A332330 u = RealDigits[t][[1]]
%t A332330 Plot[Evaluate[p[8, x]], {x, -1, 5}]
%Y A332330 Cf. A197723, A332330, A332329.
%K A332330 nonn,cons,easy
%O A332330 1,1
%A A332330 _Clark Kimberling_, Feb 11 2020