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

0,1

Links

Table of n, a(n) for n=0..99.

J. Guillera, J. Sondow, Double integrals and infinite products for some classical constants via analytic continuations of Lerch's transcendent, (2006), p. 16-17

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

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

Sequence in context: A238008 A375837 A375772 * A144481 A374172 A350550

Adjacent sequences: A193544 A193545 A193546 * A193548 A193549 A193550

Keyword

cons,nonn

Author

John M. Campbell, Jul 30 2011

Status

approved