cp's OEIS Frontend

A258870 Decimal expansion of Product_{n>=1} (1+1/n^4).

%I A258870 #21 Aug 30 2024 14:30:26
%S A258870 2,1,6,7,3,6,0,6,2,5,8,8,2,2,6,1,9,5,1,9,0,0,2,3,1,3,6,6,8,4,7,0,2,7,
%T A258870 4,4,1,8,2,1,6,1,3,1,7,2,9,6,3,4,9,8,5,0,9,7,5,6,2,3,2,5,9,9,8,8,2,2,
%U A258870 1,3,7,8,7,1,9,4,8,5,3,8,1,6,7,7,0,4,2,6,8,1,2,3,6,4,1,5,4,4,4,7,3,7,9,5,0,3,6,4,6,4,3,4,5,8,1,4,2,9,6
%N A258870 Decimal expansion of Product_{n>=1} (1+1/n^4).
%C A258870 For m>0, Product_{k>=1} (1 + m/k^4) = (cosh(sqrt(2)*Pi*m^(1/4)) - cos(sqrt(2)*Pi*m^(1/4))) / (2*Pi^2*sqrt(m)). - _Vaclav Kotesovec_, Aug 30 2024
%F A258870 Equals (cosh(sqrt(2)*Pi)-cos(sqrt(2)*Pi))/(2*Pi^2).
%F A258870 Equals exp(Sum_{j>=1} (-(-1)^j*Zeta(4*j)/j)). - _Vaclav Kotesovec_, Mar 28 2019
%e A258870 2.16736062588226195190023136684702744182161317296349850975623259988...
%p A258870 evalf((cosh(sqrt(2)*Pi)-cos(sqrt(2)*Pi))/(2*Pi^2),120);
%t A258870 RealDigits[(Cosh[Sqrt[2]*Pi]-Cos[Sqrt[2]*Pi])/(2*Pi^2),10,120][[1]]
%o A258870 (PARI) exp(sumalt(j=1, -(-1)^j*zeta(4*j)/j)) \\ _Vaclav Kotesovec_, Dec 15 2020
%Y A258870 Cf. A109219, A175615, A175617, A175619, A156648, A073017, A258871, A334411.
%K A258870 nonn,cons
%O A258870 1,1
%A A258870 _Vaclav Kotesovec_, Jun 13 2015