cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A354213 Decimal expansion of Sum_{k>=1} 1/sinh((k - 1/2)*Pi)^4.

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%I A354213 #14 May 20 2022 01:53:44
%S A354213 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 A354213 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 A354213 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 A354213 Decimal expansion of Sum_{k>=1} 1/sinh((k - 1/2)*Pi)^4.
%D A354213 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 A354213 Equals 1/(3*Pi) - Gamma(1/4)^4/(24*Pi^3) + Gamma(1/4)^8/(192*Pi^6).
%e A354213 0.035654072921285116477706132593989232850325625966390596638158946092549...
%t A354213 Join[{0}, RealDigits[1/(3*Pi) - Gamma[1/4]^4/(24*Pi^3) + Gamma[1/4]^8/(192*Pi^6), 10, 120][[1]]]
%o A354213 (PARI) suminf(k=1, 1/sinh((k - 1/2)*Pi)^4)
%Y A354213 Cf. A240964, A354214.
%K A354213 nonn,cons
%O A354213 0,2
%A A354213 _Vaclav Kotesovec_, May 19 2022