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

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.

Links

Table of n, a(n) for n=0..106.

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

Cf. A240964, A354214.

Sequence in context: A081498 A110279 A161435 * A343460 A224831 A281591

Adjacent sequences: A354210 A354211 A354212 * A354214 A354215 A354216

Keyword

nonn,cons

Author

Vaclav Kotesovec, May 19 2022

Status

approved