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A244839 Decimal expansion of the Euler double sum sum_(m>0)(sum_(n>0)((-1)^(m+n-1)/((2m-1)(m+n-1)^3))).

%I A244839 #19 Feb 16 2025 08:33:23
%S A244839 8,7,2,9,2,9,2,8,9,5,2,0,3,5,4,5,1,8,9,5,7,9,4,1,9,9,1,0,2,8,7,3,2,5,
%T A244839 3,7,3,8,2,9,9,4,5,2,0,5,3,4,3,2,4,4,5,6,8,9,3,7,1,6,2,1,1,2,1,7,0,4,
%U A244839 7,7,3,1,6,7,0,9,0,9,0,5,4,7,6,9,6,9,2,0,2,3,2,2,4,3,1,5,5,5,1,7,5,2,1,2,0
%N A244839 Decimal expansion of the Euler double sum sum_(m>0)(sum_(n>0)((-1)^(m+n-1)/((2m-1)(m+n-1)^3))).
%C A244839 The computation of this constant is given by Bailey & Borwein as an example of the use of CAS packages to check digital integrity of published mathematics.
%H A244839 Vincenzo Librandi, <a href="/A244839/b244839.txt">Table of n, a(n) for n = 0..1000</a>
%H A244839 D. H. Bailey and J. M. Borwein, <a href="http://moodle.thecarma.net/jon/ontology.pdf">Experimental computation as an ontological game changer</a>, 2014, see p. 4.
%H A244839 J. M. Borwein, I.J. Zucker and J. Boersma, <a href="http://carma.newcastle.edu.au/MZVs/mzv-week05.pdf">The evaluation of character Euler double sums</a>, The Ramanujan Journal, April 2008, Volume 15, Issue 3, pp 377-405, see p. 17.
%H A244839 Eric Weisstein's MathWorld, <a href="https://mathworld.wolfram.com/Polylogarithm.html">Polylogarithm</a>.
%F A244839 4*polylog(4, 1/2) - 151/2880*Pi^4 - Pi^2/6*log(2)^2 + 1/6*log(2)^4 + 7/2*log(2)*zeta(3).
%e A244839 0.87292928952035451895794199102873253738299452053432445689371621121704773167...
%t A244839 4*PolyLog[4, 1/2] - 151/2880*Pi^4 - Pi^2/6*Log[2]^2 + 1/6*Log[2]^4 + 7/2*Log[2]*Zeta[3] // RealDigits[#, 10, 105]& // First
%o A244839 (PARI) 151*Pi^4/2880 + Pi^2*log(2)^2/6 - 4*polylog(4, 1/2) - log(2)^4/6 - 7*log(2)*zeta(3)/2 \\ _Charles R Greathouse IV_, Aug 27 2014
%Y A244839 Cf. A099218.
%K A244839 cons,nonn
%O A244839 0,1
%A A244839 _Jean-François Alcover_, Jul 07 2014