OFFSET
0,1
REFERENCES
A. P. Prudnikov, Yu. A. Brychkov and O.I. Marichev, "Integrals and Series", Volume 1: "Elementary Functions", 1986, Eq. 6.2.4.3, p. 757.
LINKS
Eric Weisstein's World of Mathematics, Infinite Product
EXAMPLE
0.868857424887883924529781462078673655179805986254860945515526...
MAPLE
evalf(product((1 - Pi^2/(2*k^2))*sec(Pi/k), k=3..infinity), 120) # Vaclav Kotesovec, Sep 19 2014
MATHEMATICA
part1 = Product[(1 - Pi^2/(2*k^2)), {k, 3, Infinity}]; Block[{$MaxExtraPrecision = 1000}, Do[Print[N[part1/Exp[Sum[-(2^(2*n) - 1)/n*Zeta[2*n]*(Zeta[2*n] - 1 - 1/2^(2*n)), {n, 1, m}]], 130]], {m, 300, 350}]] (* Vaclav Kotesovec, Sep 20 2014 *)
PROG
(PARI) prodinf(k=3, (1 - Pi^2/(2*k^2))/cos(Pi/k)) \\ Michel Marcus, Sep 20 2014
(PARI) exp(sumpos(k=3, log((1-Pi^2/(2*k^2))/cos(Pi/k)))) \\ Converges much faster: 0.2s for 150 decimals (on i3@2.4GHz). - M. F. Hasler, Sep 20 2014
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Eric W. Weisstein, Sep 19 2014
STATUS
approved