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%I #8 Feb 12 2020 19:47:02
%S 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,
%T 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,
%U 5,0,3,7,0,5,0,3,8,6,3,5,8,3,0,4,4,4
%N Decimal expansion of the least positive zero of the 8th 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 = 1.5708210679533907291728211531492495531616658...
%t z = 150; p[n_, x_] := Normal[Series[Cos[x], {x, 0, n}]]
%t t = x /. NSolve[p[8, x] == 0, x, z][[5]]
%t u = RealDigits[t][[1]]
%t Plot[Evaluate[p[8, x]], {x, -1, 2}]
%Y Cf. A019669, A332326.
%K nonn,cons,easy
%O 1,2
%A _Clark Kimberling_, Feb 11 2020