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 A255986 Decimal expansion of Sum_{m,n >= 1} (-1)^(m + n)/(m*n*(m + n)). 0
 3, 0, 0, 5, 1, 4, 2, 2, 5, 7, 8, 9, 8, 9, 8, 5, 7, 1, 3, 4, 9, 9, 3, 4, 5, 4, 0, 3, 7, 7, 8, 6, 2, 4, 9, 7, 6, 9, 1, 2, 4, 6, 5, 7, 3, 0, 8, 5, 1, 2, 4, 7, 2, 0, 4, 4, 8, 0, 6, 7, 8, 8, 8, 8, 3, 5, 4, 5, 9, 5, 5, 1, 4, 4, 6, 5, 7, 8, 2, 7, 2, 5, 4, 6, 6, 1, 3, 9, 6, 8, 4, 0, 2, 3, 3, 3, 8, 1, 4, 5, 3, 6, 5 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 LINKS David H. Bailey and Jonathan M. Borwein, Computation and structure of character polylogarithms with applications to character Mordell-Tornheim-Witten sums, Mathematics of Computation, Vol. 85, No. 297 (2016), pp. 295-324, alternative link. FORMULA Equals zeta(3)/4 = A002117/4. From Amiram Eldar, Aug 07 2020: (Start) Equals Integral_{x=0..oo} x^2/(exp(2*x) - 1) dx. Equals Integral_{x=0..1} x * log(x)^2/(1 - x^2) dx. (End) EXAMPLE 0.30051422578989857134993454037786249769124657308512472... MAPLE evalf(Zeta(3)/4, 120); # Vaclav Kotesovec, Mar 13 2015 MATHEMATICA digits = 103; s = NSum[(-1)^(m + n)/(m*n*(m + n)), {m, 1, Infinity}, {n, 1, Infinity}, WorkingPrecision -> digits+10, Method -> "AlternatingSigns"]; RealDigits[s, 10, digits] // First RealDigits[Zeta[3]/4, 10, 100][[1]] (* Amiram Eldar, Aug 07 2020 *) CROSSREFS Cf. A002117. Sequence in context: A210953 A254280 A092669 * A011400 A115013 A072736 Adjacent sequences:  A255983 A255984 A255985 * A255987 A255988 A255989 KEYWORD nonn,cons AUTHOR Jean-François Alcover, Mar 13 2015 STATUS approved

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Last modified November 30 12:05 EST 2020. Contains 338802 sequences. (Running on oeis4.)