A118253 Decimal expansion of Product_{k>=1} sinc(2Pi/(2k+1)).

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

Offset: 0

Author

Eric W. Weisstein, Apr 18 2006

Keywords

• nonn
• cons

Examples

			0.180550541849851923912372592930506075911340235805618395412359992217663184593...
		

References

• A. P. Prudnikov, Yu. A. Brychkov, and O. I. Marichev, Integrals and Series, Vol. 1 (Overseas Publishers Association, Amsterdam, 1986), p. 757, section 6.2.4, formula 2.

Links

• Eric Weisstein's World of Mathematics, Sinc Function

Crossrefs

Cf. A051762.

Programs

Maple

evalf(Pi/(2*(product(sec(Pi/k), k = 3..infinity))), 104); # Vaclav Kotesovec, Aug 16 2015

Mathematica

digits = 102; $MaxExtraPrecision = 100; exactEnd = 100; seriesOrder = 60; f[n_] := Log[Sinc[2Pi/(2n + 1)]]; exactSum = Sum[f[n], {n, 1, exactEnd}]; se = Series[f[n], {n, Infinity, seriesOrder}] // Normal; extraSum = Sum[se, {n, exactEnd + 1, Infinity}]; RealDigits[Exp[exactSum + extraSum ], 10, digits] // First (* Jean-François Alcover, Feb 07 2013 *)

Formula

Pi/(2K), where K is given by A051762.

Extensions

Last digit corrected by Vaclav Kotesovec, Aug 16 2015