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

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, 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, 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

Offset

1,1

Comments

From Vaclav Kotesovec, Aug 30 2024: (Start)

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)).

If m tends to infinity, Product_{k>=1} (1 + m/k^6) ~ exp(2*Pi*m^(1/6)) / (8*Pi^3*sqrt(m)). (End)

Links

Table of n, a(n) for n=1..105.

Formula

Equals (cosh(Pi)-cos(sqrt(3)*Pi))*sinh(Pi)/(2*Pi^3).

Equals exp(Sum_{j>=1} (-(-1)^j*Zeta(6*j)/j)). - Vaclav Kotesovec, Mar 28 2019

Example

2.03474083500942906358682080964285089771090100623925469055753948...

Maple

evalf((cosh(Pi)-cos(sqrt(3)*Pi))*sinh(Pi)/(2*Pi^3), 120);

Mathematica

RealDigits[(Cosh[Pi]-Cos[Sqrt[3]*Pi])*Sinh[Pi]/(2*Pi^3), 10, 120][[1]]

Crossrefs

Cf. A109219, A175615, A175617, A175619, A156648, A073017, A258870, A334411.

Sequence in context: A243202 A257136 A344059 * A283528 A336972 A110990

Adjacent sequences: A258868 A258869 A258870 * A258872 A258873 A258874

Keyword

nonn,cons

Author

Vaclav Kotesovec, Jun 13 2015

Status

approved