OFFSET
0,1
FORMULA
Equals 1/2 + sqrt(2)*Pi*cos(Pi/sqrt(2))*sinh(Pi/sqrt(2))/(cosh(sqrt(2)*Pi) - cos(sqrt(2)*Pi)). - Vaclav Kotesovec, May 14 2024
EXAMPLE
0.2134154571087578332088400408966364212047132705...
MATHEMATICA
s = Sum[(-1)^k * (k^2 + 1)/(k^4 + 1), {k, 0, Infinity}]
d = Chop[N[s, 100]]
First[RealDigits[d]]
RealDigits[1/2 + Sqrt[2]*Pi*Cos[Pi/Sqrt[2]]*Sinh[Pi/Sqrt[2]] / (Cosh[Sqrt[2]*Pi] - Cos[Sqrt[2]*Pi]), 10, 120][[1]] (* Vaclav Kotesovec, May 14 2024 *)
PROG
(PARI) sumalt(k=0, (-1)^k*(k^2+1)/(k^4+1)) \\ Michel Marcus, May 15 2024
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Clark Kimberling, May 12 2024
STATUS
approved