A335415 - OEIS

%I #10 May 19 2022 08:07:00

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

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

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

%N Decimal expansion of Sum_{k>=0} 1/cosh(Pi*k).

%F Equals 1/2 + Gamma(1/4)^2 / (4*Pi^(3/2)).

%F Equals 1/2 + sqrt(Pi) / (2*Gamma(3/4)^2).

%e 1.090170299508048113022668970279244293616858317440723649757932199702152...

%p evalf(Sum(1/cosh(Pi*k), k=0..infinity), 120);

%p evalf(1/2 + sqrt(Pi) / (2*GAMMA(3/4)^2), 120);

%t RealDigits[1/2 + Gamma[1/4]^2/(4*Pi^(3/2)), 10, 120][[1]]

%o (PARI) suminf(k=0, 1/cosh(Pi*k))

%Y Cf. A240964, A254445, A335414. Essentially the same as A249205.

%K nonn,cons

%O 1,3

%A _Vaclav Kotesovec_, Jun 08 2020