A370000 - OEIS

%I #16 Feb 09 2024 03:24:28

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

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

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

%N Decimal expansion of Sum_{k>=0} (-1)^k/(3*k+2)^3.

%H R. W. Gosper, <a href="https://dspace.mit.edu/handle/1721.1/6088">Acceleration of Series</a>, Artificial Intelligence (1974) # 304.

%F Equals Sum_{n>=0} (-1)^n/A016791(n).

%F Equals A226735 - 13*zeta(3)/18 = 5*Pi^3/(2*3^(9/2)) - 13*zeta(3)/36.

%e 1/8 - 1/125 + 1/512 - 1/1331 + ... = 0.118438778425057529625616861943025438732887982...

%p 5*Pi^3/2/3^(9/2)-13*Zeta(3)/36 ; evalf(%) ;

%t RealDigits[5*Pi^3/(2*3^(9/2)) - 13*Zeta[3]/36, 10, 120][[1]] (* _Amiram Eldar_, Feb 09 2024 *)

%o (PARI) sumalt(k=0, (-1)^k/(3*k+2)^3) \\ _Michel Marcus_, Feb 07 2024

%Y Cf. A226735, A016791.

%K nonn,cons

%O 0,3

%A _R. J. Mathar_, Feb 07 2024