A247559 Product_{k>=3} (1 - Pi^2/(2*k^2))*sec(Pi/k).

8, 6, 8, 8, 5, 7, 4, 2, 4, 8, 8, 7, 8, 8, 3, 9, 2, 4, 5, 2, 9, 7, 8, 1, 4, 6, 2, 0, 7, 8, 6, 7, 3, 6, 5, 5, 1, 7, 9, 8, 0, 5, 9, 8, 6, 2, 5, 4, 8, 6, 0, 9, 4, 5, 5, 1, 5, 5, 2, 6, 0, 9, 6, 7, 7, 6, 7, 7, 9, 6, 9, 3, 6, 8, 1, 9, 2, 6, 6, 8, 4, 1, 3, 6, 7, 2, 9, 6, 4, 6, 2, 8, 0, 6, 1, 6, 8, 5, 4, 3, 9, 7, 9, 3, 6, 2

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

Table of n, a(n) for n=0..105.

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

Cf. A051762, A085365.

Sequence in context: A188655 A282152 A191909 * A246768 A088541 A362439

Adjacent sequences: A247556 A247557 A247558 * A247560 A247561 A247562

Keyword

nonn,cons

Author

Eric W. Weisstein, Sep 19 2014

Status

approved