OFFSET
1,3
FORMULA
Equals 1/2 + Gamma(1/4)^2 / (4*Pi^(3/2)).
Equals 1/2 + sqrt(Pi) / (2*Gamma(3/4)^2).
EXAMPLE
1.090170299508048113022668970279244293616858317440723649757932199702152...
MAPLE
evalf(Sum(1/cosh(Pi*k), k=0..infinity), 120);
evalf(1/2 + sqrt(Pi) / (2*GAMMA(3/4)^2), 120);
MATHEMATICA
RealDigits[1/2 + Gamma[1/4]^2/(4*Pi^(3/2)), 10, 120][[1]]
PROG
(PARI) suminf(k=0, 1/cosh(Pi*k))
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Vaclav Kotesovec, Jun 08 2020
STATUS
approved