OFFSET
0,5
LINKS
N. D. Elkies, On the sums Sum((4k+1)^(-n),k,-inf,+inf), arXiv:math/0101168 [math.CA], 2001.
N. D. Elkies, On the sums Sum_{k = -infinity .. infinity} (4k+1)^(-n), Amer. Math. Monthly, 110 (No. 7, 2003), 561-573.
Eric Weisstein's World of Mathematics, Favard Constants
FORMULA
MAPLE
HZeta := (s, v) -> Zeta(0, s, v):
a := s -> (4^s*(HZeta(-s, 1/4) - HZeta(-s, 3/4)) + HZeta(-s, 1)*(2^(s+1)-1))* 2^padic[ordp](2*(s+1), 2): seq(a(n), n = 0..28);
MATHEMATICA
a[n_] := 2^(IntegerExponent[n + 1, 2] + 1) (4^n (HurwitzZeta[-n, 1/4] - HurwitzZeta[-n, 3/4]) + HurwitzZeta[-n, 1] (2^(n + 1) - 1));
Table[FullSimplify[a[n]], {n, 0, 26}]
CROSSREFS
KEYWORD
sign
AUTHOR
Peter Luschny, Jul 20 2020
STATUS
approved