A354213 - OEIS

%I #14 May 20 2022 01:53:44

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

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

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

%N Decimal expansion of Sum_{k>=1} 1/sinh((k - 1/2)*Pi)^4.

%D A. P. Prudnikov, Yu. A. Brychkov, and O. I. Marichev, Integrals and Series, Vol. 1 (Overseas Publishers Association, Amsterdam, 1986), p. 722, section 5.3.5, formula 14.

%F Equals 1/(3*Pi) - Gamma(1/4)^4/(24*Pi^3) + Gamma(1/4)^8/(192*Pi^6).

%e 0.035654072921285116477706132593989232850325625966390596638158946092549...

%t Join[{0}, RealDigits[1/(3*Pi) - Gamma[1/4]^4/(24*Pi^3) + Gamma[1/4]^8/(192*Pi^6), 10, 120][[1]]]

%o (PARI) suminf(k=1, 1/sinh((k - 1/2)*Pi)^4)

%Y Cf. A240964, A354214.

%K nonn,cons

%O 0,2

%A _Vaclav Kotesovec_, May 19 2022