A103130 - OEIS

A103130

Decimal expansion of Integrate[(1 - x)/((1 + x y) (Log[x y])^2),{y,0,1},{x,0,1}].

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

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OFFSET

0,1

COMMENTS

Equals Integral_{u=0..1} (u - log(u) - 1)/((1 + u)*(log(u))^2). (Let u = x*y and v = y, and integrate w.r.t. v.) - Petros Hadjicostas, Jun 13 2020

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..5000

Jonathan Sondow, Double Integrals for Euler's Constant and ln(4/Pi) and an Analog of Hadjicostas's Formula, arXiv:math/0211148 [math.CA], 2002-2004.

Jonathan Sondow, Double Integrals for Euler's Constant and ln(4/Pi) and an Analog of Hadjicostas's Formula, Amer. Math. Monthly 112 (2005), 61-65.

Eric Weisstein's World of Mathematics, Hadjicostas's Formula.

FORMULA

Log[(Sqrt[Pi]*Glaisher^6)/(2^(7/6)*E)].