OFFSET
0,2
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
REFERENCES
A. P. Prudnikov, Yu. A. Brychkov, and O. I. Marichev, Integrals and Series, Vol. 1 (Overseas Publishers Association, Amsterdam, 1986).
FORMULA
Gamma(1/4)^4/(32*Pi^3) - 1/(4*Pi).
EXAMPLE
0.09457301966476193951358890085441384931495532931922401...
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 *)
PROG
(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
CROSSREFS
KEYWORD
AUTHOR
Jean-François Alcover, Aug 05 2014
STATUS
approved