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A193547
Decimal expansion of 6*log(A) - 1/2 - 2*log(2)/3, where A is the Glaisher-Kinkelin constant (A074962).
0
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
0,1
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.
EXAMPLE
0.530428...
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]
PROG
(PARI) -6*zeta'(-1)-2*log(2)/3 \\ Charles R Greathouse IV, Dec 12 2013
CROSSREFS
KEYWORD
cons,nonn
AUTHOR
John M. Campbell, Jul 30 2011
STATUS
approved