A394965 - OEIS

%I #7 Apr 08 2026 10:39:01

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

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

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

%N Decimal expansion of Pi^3/360.

%H H. F. Sandham, <a href="https://doi.org/10.1090/S0002-9939-1954-0062248-X">Some infinite series</a>, Proc. Amer. Math. Soc., Vol. 5 (1954), pp. 430-436.

%F Equals Sum_{k>=1} (-1)^(k+1)/(k^3*sinh(k*Pi)) (Sandham, 1954, p. 430, eq. 1.32). Note that equation 1.32 has an error: the powers 1^5, 2^5, 3^5, ... should be 1^3, 2^3, 3^3, ... .

%e 0.08612854633416616715410087518639276445062580157190307...

%t RealDigits[Pi^3/360, 10, 120, -1][[1]]

%o (PARI) Pi^3/360

%Y Cf. A091925, A394964.

%K nonn,cons

%O 0,2

%A _Amiram Eldar_, Apr 08 2026