A240964 Decimal expansion of Sum_{n>=1} n/sinh(n*Pi).

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

Offset: 0

Author

Jean-François Alcover, Aug 05 2014

Keywords

• nonn
• cons
• easy

Comments

Prudnikov (p. 721, section 5.3.5, formula 1) has a typo, Gamma(1/4)^4 is correct, not Gamma(1/4)^2. - Vaclav Kotesovec, May 19 2022

Examples

			0.09457301966476193951358890085441384931495532931922401...
		

References

• A. P. Prudnikov, Yu. A. Brychkov, and O. I. Marichev, Integrals and Series, Vol. 1 (Overseas Publishers Association, Amsterdam, 1986).

Crossrefs

Cf. A068466, A335414, A335415.

Programs

Mathematica

Join[{0}, RealDigits[Gamma[1/4]^4/(32*Pi^3) - 1/(4*Pi), 10, 100] // First]
N[EllipticK[k]/Pi^2*(EllipticK[k] - EllipticE[k]) /. k -> 1/2, 100] (* Vaclav Kotesovec, May 19 2022 *)

PARI

suminf(k=1, k/sinh(k*Pi)) \\ Vaclav Kotesovec, May 19 2022

PARI

suminf(k=1, 1/(2*sinh((k - 1/2)*Pi)^2)) \\ Vaclav Kotesovec, May 19 2022

Formula

Gamma(1/4)^4/(32*Pi^3) - 1/(4*Pi).