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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))). 2


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

%C 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 Vincenzo Librandi, <a href="/A244839/b244839.txt">Table of n, a(n) for n = 0..1000</a>

%H 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 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 Eric Weisstein's MathWorld, <a href="http://mathworld.wolfram.com/Polylogarithm.html">Polylogarithm</a>.

%F 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 0.87292928952035451895794199102873253738299452053432445689371621121704773167...

%t 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 (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 Cf. A099218.

%K cons,nonn

%O 0,1

%A _Jean-Fran├žois Alcover_, Jul 07 2014

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Last modified December 7 18:12 EST 2019. Contains 329847 sequences. (Running on oeis4.)