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A118253
Decimal expansion of Product_{k>=1} sinc(2Pi/(2k+1)).
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
0,2
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
FORMULA
Pi/(2K), where K is given by A051762.
EXAMPLE
0.180550541849851923912372592930506075911340235805618395412359992217663184593...
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 *)
CROSSREFS
Cf. A051762.
Sequence in context: A021558 A335958 A308739 * A135001 A146293 A019724
KEYWORD
nonn,cons
AUTHOR
Eric W. Weisstein, Apr 18 2006
EXTENSIONS
Last digit corrected by Vaclav Kotesovec, Aug 16 2015
STATUS
approved