OFFSET
1,1
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
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
EXAMPLE
2.16736062588226195190023136684702744182161317296349850975623259988...
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]]
PROG
(PARI) exp(sumalt(j=1, -(-1)^j*zeta(4*j)/j)) \\ Vaclav Kotesovec, Dec 15 2020
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Vaclav Kotesovec, Jun 13 2015
STATUS
approved