cp's OEIS Frontend

A332326 Decimal expansion of the least positive zero of the 4th Maclaurin polynomial of cos x.

%I A332326 #8 Feb 12 2020 19:45:30
%S A332326 1,5,9,2,4,5,0,4,3,4,0,3,6,2,5,1,3,8,1,6,6,8,9,9,8,6,7,0,4,8,4,0,0,1,
%T A332326 9,6,9,6,5,9,5,5,0,5,6,2,7,0,7,2,2,1,7,1,8,2,1,7,6,8,6,4,5,5,1,7,7,5,
%U A332326 6,6,8,0,7,6,2,1,2,2,5,3,4,1,3,2,9,1
%N A332326 Decimal expansion of the least positive zero of the 4th Maclaurin polynomial of cos x.
%C A332326 The Maclaurin polynomial p(2n,x) of cos x is 1 - x^2/2! + x^4/4! + ... + (-1)^n  ^(2n)/(2n)!.
%C A332326 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 A332326 Least positive zero = 1.592450434036251381668998670484001969...
%t A332326 z = 150; p[n_, x_] := Normal[Series[Cos[x], {x, 0, n}]]
%t A332326 t = x /. NSolve[p[4, x] == 0, x, z][[3]]
%t A332326 u = RealDigits[t][[1]]
%t A332326 Plot[Evaluate[p[4, x]], {x, -1, 4}]
%Y A332326 Cf. A019669, A332325, A332327, A323328, A323329.
%K A332326 nonn,cons,easy
%O A332326 1,2
%A A332326 _Clark Kimberling_, Feb 11 2020