cp's OEIS Frontend

A079059 Decimal expansion of product( p == 3 (mod 4), sqrt(1-p^-2)).

%I A079059 #20 Nov 06 2016 11:35:47
%S A079059 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 A079059 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 A079059 9,7,5,3,2,7,7,0,3,5,1,4,1,6,8,0,4,9,5
%N A079059 Decimal expansion of product( p == 3 (mod 4), sqrt(1-p^-2)).
%C A079059 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 A079059 E. Landau, "Handbuch der Lehre von der Verteilung der Primzahlen", vol. 2, Teubner, Leipzig; third edition: Chelsea, New York (1974), pp. 641-669
%H A079059 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 A079059 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 A079059 product( p == 3 (mod 4), sqrt(1-p^-2)) = 0.92526...
%F A079059 Equals 1/(sqrt(2)*A064533) = A010503/A064533. [_R. J. Mathar_, Jul 29 2010]
%o A079059 (PARI) prod(k=1,40000,if(prime(k)%4-3,1,sqrt(1-prime(k)^-2)))
%Y A079059 Cf. A071903.
%K A079059 cons,nonn
%O A079059 0,1
%A A079059 _Benoit Cloitre_, Feb 02 2003
%E A079059 Corrected offset and leading zero _R. J. Mathar_, Jan 31 2009
%E A079059 More digits from _R. J. Mathar_, Jul 28 2010
%E A079059 More digits, using the Jul 29 2010 formula from _R. J. Mathar_, from _Jon E. Schoenfield_, Nov 05 2016