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%I #8 Feb 12 2020 19:46:06
%S 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 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 3,4,4,5,3,2,4,4,6,5,2,7,2,8,2,5,6,2
%N Decimal expansion of the least positive zero of the 6th 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 least positive zero of p(2n,x). The limit of z(n) is Pi/2 = 1.570796326..., as in A019669.
%e Least positive zero = 1.56990582516119145661812218578182974...
%t z = 150; p[n_, x_] := Normal[Series[Cos[x], {x, 0, n}]]
%t t = x /. NSolve[p[6, x] == 0, x, z][[4]]
%t u = RealDigits[t][[1]]
%t Plot[Evaluate[p[6, x]], {x, -1, 2}]
%Y Cf. A019669, A332326.
%K nonn,cons,easy
%O 1,2
%A _Clark Kimberling_, Feb 11 2020
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