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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 (list; constant; graph; refs; listen; history; text; internal format)
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: A322758 A077602 A238008 * A144481 A232225 A200126

Adjacent sequences:  A193544 A193545 A193546 * A193548 A193549 A193550

KEYWORD

cons,nonn

AUTHOR

John M. Campbell, Jul 30 2011

STATUS

approved

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Last modified March 18 19:55 EDT 2019. Contains 321293 sequences. (Running on oeis4.)