A193547 Decimal expansion of 6*log(A) - 1/2 - 2*log(2)/3, where A is the Glaisher-Kinkelin constant (A074962).
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, 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, 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
Offset: 0
Examples
0.530428...
Links
- J. Guillera, J. Sondow, Double integrals and infinite products for some classical constants via analytic continuations of Lerch's transcendent, (2006), p. 16-17
Programs
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Mathematica
N[-Integrate[(x (4 x^2 - x^4))/((-2 + x^2)^2 Log[1 - x^2]), {x, 0, 1}]] RealDigits[-(1/2) - (2 Log[2])/3 + 6 Log[Glaisher], 10, 200] -
PARI
-6*zeta'(-1)-2*log(2)/3 \\ Charles R Greathouse IV, Dec 12 2013
Formula
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.