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

Author

Jean-François Alcover, Jul 07 2014

Keywords

• cons
• nonn

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.

Examples

			0.87292928952035451895794199102873253738299452053432445689371621121704773167...
		

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.

Crossrefs

Cf. A099218.

Programs

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

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

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).