A387915 - OEIS

%I #30 Jul 08 2026 22:53:11

%S 0,0,1,1,4,4,8,4,0,8,9,1,1,3,9,1,0,7,2,7,8,4,1,1,2,4,7,5,6,8,1,2,1,5,

%T 3,6,1,7,9,5,3,6,0,4,8,0,2,6,4,4,0,8,7,8,2,7,9,5,2,1,0,3,0,4,6,5,3,2,

%U 9,7,0,0,9,1,5,5,1,2,5,7,1,7,5,0,2,7,7,6,5,5,4,7,8,8,6,0,7,8,2,5

%N Decimal expansion of Sum_{k>=1} 1/(12*k-2)^3.

%H Michael I. Shamos, <a href="https://citeseerx.ist.psu.edu/pdf/ae33a269baba5e8b1038e719fb3209e8a00abec5">Shamos's Catalog of the Real Numbers</a>, 2011, p. 29.

%F Equals (-1/3456) * PolyGamma(2, 5/6).

%F Equals (91*zeta(3) - 2*sqrt(3)*Pi^3)/1728. - _Vaclav Kotesovec_, Oct 18 2025

%e 0.00114484089113910727841124756812153617953604802644087827...

%t First[RealDigits[-1/3456 * PolyGamma[2, 5/6], 10, 100, -1]]

%t RealDigits[(91*Zeta[3] - 2*Sqrt[3]*Pi^3)/1728, 10, 100, -1][[1]] (* _Vaclav Kotesovec_, Oct 18 2025 *)

%o (PARI) zetahurwitz(3, 5/6)/1728 \\ _Charles R Greathouse IV_, Jul 08 2026

%K nonn,cons,changed

%O 0,5

%A _Jason Bard_, Oct 16 2025