A193547 - OEIS

%I #13 Dec 12 2013 08:40:33

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

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

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

%N Decimal expansion of 6*log(A) - 1/2 - 2*log(2)/3, where A is the Glaisher-Kinkelin constant (A074962).

%H J. Guillera, J. Sondow, <a href="http://arxiv.org/abs/math/0506319">Double integrals and infinite products for some classical constants via analytic continuations of Lerch's transcendent</a>, (2006), p. 16-17

%F Equals: -integral(x=0..1,  x*(4*x^2 - x^4) / ((-2 + x^2)^2 * log(1 - x^2)) ). See Guillera & Sondow link for a related product.

%e 0.530428...

%t N[-Integrate[(x (4 x^2 - x^4))/((-2 + x^2)^2 Log[1 - x^2]), {x, 0,  1}]]

%t RealDigits[-(1/2) - (2 Log[2])/3 + 6 Log[Glaisher], 10, 200]

%o (PARI) -6*zeta'(-1)-2*log(2)/3 \\ _Charles R Greathouse IV_, Dec 12 2013

%Y Cf. A074962, A115521, A099791, A099792, A087501, A175820.

%K cons,nonn

%O 0,1

%A _John M. Campbell_, Jul 30 2011