A332331 - OEIS

%I #10 Feb 12 2020 19:48:51

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

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

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

%N Decimal expansion of the next-to-least positive zero of the 12th 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 = 4.6865176637957574465700489837907750...

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

%t t = x /. NSolve[p[12, x] == 0, x, z][[8]]

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

%t Plot[Evaluate[p[12, x]], {x, -1, 5}]

%Y Cf. A197723, A332329, A332330.

%K nonn,cons,easy

%O 1,1

%A _Clark Kimberling_, Feb 11 2020