cp's OEIS Frontend

A335415 Decimal expansion of Sum_{k>=0} 1/cosh(Pi*k).

%I A335415 #10 May 19 2022 08:07:00
%S A335415 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 A335415 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 A335415 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 A335415 Decimal expansion of Sum_{k>=0} 1/cosh(Pi*k).
%F A335415 Equals 1/2 + Gamma(1/4)^2 / (4*Pi^(3/2)).
%F A335415 Equals 1/2 + sqrt(Pi) / (2*Gamma(3/4)^2).
%e A335415 1.090170299508048113022668970279244293616858317440723649757932199702152...
%p A335415 evalf(Sum(1/cosh(Pi*k), k=0..infinity), 120);
%p A335415 evalf(1/2 + sqrt(Pi) / (2*GAMMA(3/4)^2), 120);
%t A335415 RealDigits[1/2 + Gamma[1/4]^2/(4*Pi^(3/2)), 10, 120][[1]]
%o A335415 (PARI) suminf(k=0, 1/cosh(Pi*k))
%Y A335415 Cf. A240964, A254445, A335414. Essentially the same as A249205.
%K A335415 nonn,cons
%O A335415 1,3
%A A335415 _Vaclav Kotesovec_, Jun 08 2020