cp's OEIS Frontend

A258871 Decimal expansion of Product_{n>=1} (1+1/n^6).

%I A258871 #17 Feb 04 2025 15:08:07
%S A258871 2,0,3,4,7,4,0,8,3,5,0,0,9,4,2,9,0,6,3,5,8,6,8,2,0,8,0,9,6,4,2,8,5,0,
%T A258871 8,9,7,7,1,0,9,0,1,0,0,6,2,3,9,2,5,4,6,9,0,5,5,7,5,3,9,4,8,0,4,5,2,9,
%U A258871 8,4,1,2,0,1,9,1,5,2,5,8,4,9,1,3,5,3,5,9,8,1,5,4,9,6,6,7,0,7,6,8,6,7,8,1,3
%N A258871 Decimal expansion of Product_{n>=1} (1+1/n^6).
%C A258871 From _Vaclav Kotesovec_, Aug 30 2024: (Start)
%C A258871 For m>0, Product_{k>=1} (1 + m/k^6) = (cosh(Pi*m^(1/6)) - cos(sqrt(3)*Pi*m^(1/6))) * sinh(Pi*m^(1/6)) / (2*Pi^3*sqrt(m)).
%C A258871 If m tends to infinity, Product_{k>=1} (1 + m/k^6) ~ exp(2*Pi*m^(1/6)) / (8*Pi^3*sqrt(m)). (End)
%F A258871 Equals (cosh(Pi)-cos(sqrt(3)*Pi))*sinh(Pi)/(2*Pi^3).
%F A258871 Equals exp(Sum_{j>=1} (-(-1)^j*Zeta(6*j)/j)). - _Vaclav Kotesovec_, Mar 28 2019
%e A258871 2.03474083500942906358682080964285089771090100623925469055753948...
%p A258871 evalf((cosh(Pi)-cos(sqrt(3)*Pi))*sinh(Pi)/(2*Pi^3), 120);
%t A258871 RealDigits[(Cosh[Pi]-Cos[Sqrt[3]*Pi])*Sinh[Pi]/(2*Pi^3),10,120][[1]]
%o A258871 (PARI) prodnumrat(1+x^-6, 1) \\ _Charles R Greathouse IV_, Feb 04 2025
%Y A258871 Cf. A109219, A175615, A175617, A175619, A156648, A073017, A258870, A334411.
%K A258871 nonn,cons
%O A258871 1,1
%A A258871 _Vaclav Kotesovec_, Jun 13 2015