|
|
A332326
|
|
Decimal expansion of the least positive zero of the 4th Maclaurin polynomial of cos x.
|
|
3
|
|
|
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, 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, 6, 6, 8, 0, 7, 6, 2, 1, 2, 2, 5, 3, 4, 1, 3, 2, 9, 1
(list;
constant;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
COMMENTS
|
The Maclaurin polynomial p(2n,x) of cos x is 1 - x^2/2! + x^4/4! + ... + (-1)^n ^(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.
|
|
LINKS
|
|
|
EXAMPLE
|
Least positive zero = 1.592450434036251381668998670484001969...
|
|
MATHEMATICA
|
z = 150; p[n_, x_] := Normal[Series[Cos[x], {x, 0, n}]]
t = x /. NSolve[p[4, x] == 0, x, z][[3]]
u = RealDigits[t][[1]]
Plot[Evaluate[p[4, x]], {x, -1, 4}]
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|