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Decimal expansion of Pi^2/(16*K^2*G) = Product_{p prime congruent to 3 modulo 4} (1 + 1/p^2), where K is the Landau-Ramanujan constant and G Catalan's constant.
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%I #24 Apr 30 2020 03:40:09

%S 1,1,5,3,0,8,0,5,6,1,5,8,5,4,4,7,8,7,0,3,6,5,2,5,8,0,6,8,5,6,1,7,6,3,

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

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

%N Decimal expansion of Pi^2/(16*K^2*G) = Product_{p prime congruent to 3 modulo 4} (1 + 1/p^2), where K is the Landau-Ramanujan constant and G Catalan's constant.

%D Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 2.3 Landau-Ramanujan constant, p. 101.

%H G. C. Greubel, <a href="/A243381/b243381.txt">Table of n, a(n) for n = 1..2500</a>

%H Eric Weisstein's MathWorld, <a href="http://mathworld.wolfram.com/Landau-RamanujanConstant.html">Ramanujan constant</a>

%H Eric Weisstein's MathWorld, <a href="http://mathworld.wolfram.com/CatalansConstant.html">Catalan's Constant</a>

%F Pi^2/(16*K^2*G), where K is the Landau-Ramanujan constant (A064533) and G Catalan's constant (A006752).

%F A243380 * A243381 = 12/Pi^2. - _Vaclav Kotesovec_, Apr 30 2020

%e 1.1530805615854478703652580685617633651...

%t digits = 101; LandauRamanujanK = 1/Sqrt[2]*NProduct[((1 - 2^(-2^n))*Zeta[2^n]/DirichletBeta[2^n])^(1/2^(n + 1)), {n, 1, 24}, WorkingPrecision -> digits + 5]; Pi^2/(16*LandauRamanujanK^2*Catalan) // RealDigits[#, 10, digits] & // First (* updated Mar 14 2018 *)

%Y Cf. A002145, A064533, A243379.

%K nonn,cons

%O 1,3

%A _Jean-François Alcover_, Jun 04 2014