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%I #20 Nov 06 2016 11:35:47
%S 9,2,5,2,6,1,5,7,4,7,5,7,0,4,8,6,2,2,6,2,7,0,7,0,4,2,2,9,6,6,9,6,3,4,
%T 4,2,6,4,2,4,7,3,4,7,8,7,8,8,6,5,1,1,1,4,0,6,6,3,3,0,8,8,5,9,9,1,9,5,
%U 9,7,5,3,2,7,7,0,3,5,1,4,1,6,8,0,4,9,5
%N Decimal expansion of product( p == 3 (mod 4), sqrt(1-p^-2)).
%C The complementary product_{p == 1 (mod 4)} sqrt(1-1/p^2) = 0.97303... is related: 0.925261....*0.97303... = sqrt(4/3)/sqrt(Zeta(2)) = 10*A020832/sqrt(A013661). [_R. J. Mathar_, Jan 31 2009]
%D E. Landau, "Handbuch der Lehre von der Verteilung der Primzahlen", vol. 2, Teubner, Leipzig; third edition: Chelsea, New York (1974), pp. 641-669
%H E. Landau, <a href="http://www.hti.umich.edu/cgi/t/text/text-idx?sid=b88432273f115fb346725f1a42422e19;c=umhistmath;idno=ABV2766.0002.001">Handbuch der Lehre von der Verteilung der Primzahlen</a>, vol. 2, Leipzig, Berlin, B. G. Teubner, 1909.
%H E. Landau, Handbuch der Lehre von der Verteilung der Primzahlen, <a href="http://name.umdl.umich.edu/ABV2766.0001.001">vol. 1</a> and <a href="http://name.umdl.umich.edu/ABV2766.0002.001">vol. 2</a>, Leipzig, Berlin, B. G. Teubner, 1909.
%F product( p == 3 (mod 4), sqrt(1-p^-2)) = 0.92526...
%F Equals 1/(sqrt(2)*A064533) = A010503/A064533. [_R. J. Mathar_, Jul 29 2010]
%o (PARI) prod(k=1,40000,if(prime(k)%4-3,1,sqrt(1-prime(k)^-2)))
%Y Cf. A071903.
%K cons,nonn
%O 0,1
%A _Benoit Cloitre_, Feb 02 2003
%E Corrected offset and leading zero _R. J. Mathar_, Jan 31 2009
%E More digits from _R. J. Mathar_, Jul 28 2010
%E More digits, using the Jul 29 2010 formula from _R. J. Mathar_, from _Jon E. Schoenfield_, Nov 05 2016
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