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 A244843 Decimal expansion of the integral of log(2+x^2+y^2)/((1+x^2)*(1+y^2)) dx dy over the square [0,1]x[0,1]. 2
 5, 6, 9, 5, 9, 6, 1, 5, 8, 1, 8, 3, 6, 1, 4, 5, 0, 6, 2, 3, 6, 4, 5, 5, 5, 3, 6, 7, 2, 7, 1, 7, 4, 6, 9, 0, 1, 0, 7, 8, 7, 6, 1, 2, 6, 8, 2, 1, 2, 2, 8, 7, 8, 3, 6, 8, 2, 8, 1, 8, 4, 0, 8, 1, 2, 4, 8, 5, 2, 3, 0, 0, 2, 5, 0, 2, 9, 9, 1, 8, 1, 1, 6, 1, 4, 0, 5, 6, 5, 7, 4, 2, 2, 2, 7, 2, 4, 5, 8, 6, 8 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS The computation of this integral is given by Bailey & Borwein as an example of the use of CAS packages (and additional tools) to simplify large symbolic expressions. 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. 5. D. H. Bailey, J. M. Borwein and A. D. Kaiser, Automated Simplification of Large Symbolic Expressions Eric Weisstein's MathWorld, Clausen's Integral. Eric Weisstein's MathWorld, Polylogarithm. FORMULA Pi^2/8*log(2) - 7/48*zeta(3) + 11/24*Pi*Cl2(Pi/6) - 29/24*Pi*Cl2(5*Pi/6), where Cl2 is the Clausen function Cl2(t) = Sum_{n>0} sin(n*t)/n^2. EXAMPLE 0.56959615818361450623645553672717469010787612682122878368281840812485230025... MATHEMATICA Clausen2[x_] := Im[PolyLog[2, Exp[x*I]]]; Pi^2/8*Log[2] - 7/48*Zeta[3] + 11/24*Pi*Clausen2[Pi/6] - 29/24*Pi*Clausen2[5*Pi/6] // RealDigits[#, 10, 101]& // First PROG (PARI) Cl2(x)=imag(polylog(2, exp(x*I))); Pi^2/8*log(2) - 7/48*zeta(3) + 11/24*Pi*Cl2(Pi/6) - 29/24*Pi*Cl2(5*Pi/6) \\ Charles R Greathouse IV, Aug 27 2014 CROSSREFS Cf. A261027 (Cl_2(Pi/6)), A261028 (Cl_2(5*Pi/6)). Sequence in context: A277522 A019598 A197283 * A118261 A246749 A021641 Adjacent sequences:  A244840 A244841 A244842 * A244844 A244845 A244846 KEYWORD cons,nonn AUTHOR Jean-François Alcover, Jul 07 2014 STATUS approved

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Last modified April 23 07:51 EDT 2019. Contains 322381 sequences. (Running on oeis4.)