A247444 - OEIS

%I #14 Jan 17 2020 16:14:46

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

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

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

%N Decimal expansion of the infinite product of (1-1/n^2)^(n^2)/(1-1/(4*n^2))^(4*n^2) for n >= 2.

%H Steven R. Finch, <a href="http://arxiv.org/abs/2001.00578">Errata and Addenda to Mathematical Constants.</a> p. 2.

%H S. R. Holcombe, <a href="http://arxiv.org/abs/1204.2451">A product representation for Pi</a>, arXiv:1204.2451 [math.NT], 2012.

%F Equals (2^9/9^2)*Pi*exp(7*zeta(3)/(2*Pi^2)) = A240984 / A240985.

%e 0.76119387834763207605237256389850699513971912053...

%p evalf(product((1-1/n^2)^(n^2)/(1-1/(4*n^2))^(4*n^2), n=2..infinity), 100) # _Vaclav Kotesovec_, Sep 17 2014

%t RealDigits[(9^2/2^9)*Pi*Exp[7*Zeta[3]/(2*Pi^2)], 10, 100] // First

%Y Cf. A240984.

%K nonn,cons,easy

%O 0,1

%A _Jean-François Alcover_, Sep 17 2014