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

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

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