cp's OEIS Frontend

A332327 Decimal expansion of the least positive zero of the 6th Maclaurin polynomial of cos x.

%I A332327 #8 Feb 12 2020 19:46:06
%S A332327 1,5,6,9,9,0,5,8,2,5,1,6,1,1,9,1,4,5,6,6,1,8,1,2,2,1,8,5,7,8,1,8,2,9,
%T A332327 7,4,8,3,7,2,4,5,2,3,2,5,4,9,7,3,1,6,8,3,7,1,2,4,8,9,5,4,6,9,2,0,0,6,
%U A332327 3,4,4,5,3,2,4,4,6,5,2,7,2,8,2,5,6,2
%N A332327 Decimal expansion of the least positive zero of the 6th Maclaurin polynomial of cos x.
%C A332327 The Maclaurin polynomial p(2n,x) of cos x is 1 - x^2/2! + x^4/4! + ... + (-1)^n x^(2n)/(2n)!.
%C A332327 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.
%e A332327 Least positive zero = 1.56990582516119145661812218578182974...
%t A332327 z = 150; p[n_, x_] := Normal[Series[Cos[x], {x, 0, n}]]
%t A332327 t = x /. NSolve[p[6, x] == 0, x, z][[4]]
%t A332327 u = RealDigits[t][[1]]
%t A332327 Plot[Evaluate[p[6, x]], {x, -1, 2}]
%Y A332327 Cf. A019669, A332326.
%K A332327 nonn,cons,easy
%O A332327 1,2
%A A332327 _Clark Kimberling_, Feb 11 2020