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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
 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, 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, 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 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS 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. LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..1000 D. H. Bailey and J. M. Borwein, Experimental computation as an ontological game changer, 2014, see p. 4. J. M. Borwein, I.J. Zucker and J. Boersma, The evaluation of character Euler double sums, The Ramanujan Journal, April 2008, Volume 15, Issue 3, pp 377-405, see p. 17. Eric Weisstein's MathWorld, Polylogarithm. FORMULA 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). EXAMPLE 0.87292928952035451895794199102873253738299452053432445689371621121704773167... MATHEMATICA 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 PROG (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 CROSSREFS Cf. A099218. Sequence in context: A144750 A198928 A155068 * A329450 A203069 A343626 Adjacent sequences:  A244836 A244837 A244838 * A244840 A244841 A244842 KEYWORD cons,nonn AUTHOR Jean-François Alcover, Jul 07 2014 STATUS approved

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Last modified January 21 03:58 EST 2022. Contains 350473 sequences. (Running on oeis4.)