login
A182448
Decimal expansion of Pi^2/15.
15
6, 5, 7, 9, 7, 3, 6, 2, 6, 7, 3, 9, 2, 9, 0, 5, 7, 4, 5, 8, 8, 9, 6, 6, 0, 6, 6, 6, 5, 8, 4, 1, 0, 0, 7, 5, 6, 8, 7, 5, 7, 9, 9, 6, 0, 4, 8, 2, 7, 1, 9, 3, 7, 5, 0, 9, 4, 2, 2, 3, 2, 9, 1, 7, 4, 8, 0, 0, 2, 9, 8, 8, 1, 6, 1, 2, 8, 0, 3, 4, 9, 5, 3, 3, 4, 5, 1, 5, 6, 0, 2, 4, 7, 9, 0, 3, 4, 8, 2, 1, 2, 1, 6, 0, 1
OFFSET
0,1
LINKS
László Tóth, Linear combinations of Dirichlet series associated with the Thue-Morse sequence, Integers: Electronic Journal of Combinatorial Number Theory, Vol. 22 (2022), #A98; arXiv preprint, arXiv:2211.13570 [math.NT], 2022.
FORMULA
See Mathematica code.
Equals Gamma(4)*zeta(4)/Pi^2 = zeta(4)/zeta(2) = A013662/A013661 = Product_{p prime} (p^2/(p^2+1)). - Stanislav Sykora, Oct 21 2014
Equals (1/10) * Sum_{n >= 0} (-1)^n*( 1/(n + 1/3)^2 - 1/(n + 2/3)^2 ). - Peter Bala, Oct 31 2019
Equals Sum_{k>=1} A008836(k)/k^2. - Amiram Eldar, Jun 23 2020
Equals (1/10) * Sum_{k>=1} (5*t(k-1) + 3*t(k))/k^2, where t(k) = A010060(k) (Tóth, 2022). - Amiram Eldar, Feb 04 2024
EXAMPLE
0.65797362673929...
MATHEMATICA
RealDigits[N[Sum[1/(n + 0)^2 - 1/(n + 1)^2 + 1/(n + 2)^2 - 1/(n + 3)^2 - 4/(n + 4)^2 - 1/(n + 5)^2 + 1/(n + 6)^2 - 1/(n + 7)^2 + 1/(n + 8)^2 + 4/(n + 9)^2, {n, 1, Infinity, 10}], 90]][[1]]
RealDigits[N[Sum[LiouvilleLambda[n]/n^2, {n, 1, Infinity}], 90]][[1]]
RealDigits[Pi^2/15, 10, 120][[1]] (* Harvey P. Dale, May 28 2017 *)
PROG
(PARI) Pi^2/15 \\ Michel Marcus, Oct 21 2014
KEYWORD
nonn,cons
AUTHOR
Mats Granvik, Apr 29 2012
EXTENSIONS
Offset corrected and more terms added by Rick L. Shepherd, Jan 08 2014
STATUS
approved