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

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, 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, 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

Offset: 1

Author

Vaclav Kotesovec, Jun 13 2015

Keywords

• nonn
• cons

Comments

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

Examples

			2.16736062588226195190023136684702744182161317296349850975623259988...
		

Crossrefs

Cf. A109219, A175615, A175617, A175619, A156648, A073017, A258871, A334411.

Programs

Maple

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

Mathematica

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

PARI

exp(sumalt(j=1, -(-1)^j*zeta(4*j)/j)) \\ Vaclav Kotesovec, Dec 15 2020

Formula

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

Equals exp(Sum_{j>=1} (-(-1)^j*Zeta(4*j)/j)). - Vaclav Kotesovec, Mar 28 2019