OFFSET
1,2
COMMENTS
The Maclaurin polynomial p(2n,x) of cos x is 1 - x^2/2! + x^4/4! + ... + (-1)^n x^(2n)/(2n)!.
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.
EXAMPLE
Least positive zero = 1.5708210679533907291728211531492495531616658...
MATHEMATICA
z = 150; p[n_, x_] := Normal[Series[Cos[x], {x, 0, n}]]
t = x /. NSolve[p[8, x] == 0, x, z][[5]]
u = RealDigits[t][[1]]
Plot[Evaluate[p[8, x]], {x, -1, 2}]
CROSSREFS
KEYWORD
AUTHOR
Clark Kimberling, Feb 11 2020
STATUS
approved