|
|
A210245
|
|
Signs of the polylogarithm li(-n,-1/2).
|
|
3
|
|
|
1, -1, -1, 1, 1, -1, -1, -1, 1, 1, -1, -1, 1, 1, 1, -1, -1, 1, 1, -1, -1, -1, 1, 1, -1, -1, 1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, 1, -1, -1, 1, 1, -1, -1, -1, 1, 1, -1, -1, 1, 1, 1, -1, -1, 1, 1, -1, -1, -1, 1, 1, -1, -1, 1, 1, 1, -1, -1, 1, 1, -1, -1, -1, 1, 1
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0
|
|
COMMENTS
|
Given an integer n, consider the infinite series s(n) = li(-n,-1/2)) = Sum((-1)^k)(k^n)/2^k) for k=0,1,2,... Then the value of a(n) is the sign of s(n).
Should s(n) be 0, the sign would be set to 0 as well. However, it is not known whether this ever happens.
|
|
LINKS
|
|
|
FORMULA
|
a(n) is the same as the sign of cos((n+1)*arctan(Pi/log(2))). - Mikhail Kurkov, Apr 13 2021 [verification needed]
|
|
EXAMPLE
|
a(5) = sign(A212846(5)) = sign(-7) = -1.
|
|
MATHEMATICA
|
Join[{1}, Sign[PolyLog[-Range[80], -1/2]]] (* Harvey P. Dale, Jul 21 2024 *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
sign
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|