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

%I #9 May 20 2022 01:54:57

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

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

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

%N Decimal expansion of Sum_{k>=1} 1/sinh(k*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 13.

%F Equals -11/90 + 1/(3*Pi) + Gamma(1/4)^8/(1920*Pi^6).

%e 0.000056216419804771873282753399441455661110814777284338006432106020376...

%t RealDigits[-11/90 + 1/(3*Pi) + Gamma[1/4]^8/(1920*Pi^6), 10, 120][[1]]

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

%Y Cf. A110191, A254446, A335414, A335415, A354213.

%K nonn,cons

%O -4,1

%A _Vaclav Kotesovec_, May 19 2022