login
A354213
Decimal expansion of Sum_{k>=1} 1/sinh((k - 1/2)*Pi)^4.
1
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, 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, 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
OFFSET
0,2
REFERENCES
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.
FORMULA
Equals 1/(3*Pi) - Gamma(1/4)^4/(24*Pi^3) + Gamma(1/4)^8/(192*Pi^6).
EXAMPLE
0.035654072921285116477706132593989232850325625966390596638158946092549...
MATHEMATICA
Join[{0}, RealDigits[1/(3*Pi) - Gamma[1/4]^4/(24*Pi^3) + Gamma[1/4]^8/(192*Pi^6), 10, 120][[1]]]
PROG
(PARI) suminf(k=1, 1/sinh((k - 1/2)*Pi)^4)
CROSSREFS
Sequence in context: A081498 A110279 A161435 * A343460 A224831 A281591
KEYWORD
nonn,cons
AUTHOR
Vaclav Kotesovec, May 19 2022
STATUS
approved