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

%I #18 May 23 2022 06:45:37

%S 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,

%T 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,

%U 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

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

%D 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.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/SincFunction.html">Sinc Function</a>

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

%e 0.180550541849851923912372592930506075911340235805618395412359992217663184593...

%p evalf(Pi/(2*(product(sec(Pi/k), k = 3..infinity))), 104); # _Vaclav Kotesovec_, Aug 16 2015

%t 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 *)

%Y Cf. A051762.

%K nonn,cons

%O 0,2

%A _Eric W. Weisstein_, Apr 18 2006

%E Last digit corrected by _Vaclav Kotesovec_, Aug 16 2015

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