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 A196878 Decimal expansion of Pi/8*(6*zeta(3)+Pi^2*log(2)+4*log(2)^3). 3
 6, 0, 4, 1, 8, 8, 2, 9, 0, 9, 7, 7, 5, 0, 9, 3, 5, 2, 2, 1, 5, 0, 4, 2, 4, 1, 3, 0, 6, 7, 5, 9, 9, 5, 9, 8, 5, 5, 0, 8, 7, 1, 0, 3, 0, 5, 7, 7, 4, 6, 4, 1, 9, 0, 7, 2, 5, 8, 6, 0, 1, 0, 1, 5, 2, 6, 0, 0, 4, 3, 0, 2, 5, 4, 6, 5, 5, 7, 5, 8, 1, 6, 0, 4, 0, 4, 7, 0, 8, 2, 6, 5, 8, 8, 2, 6, 1, 6, 9, 5, 1, 5, 5, 8, 1 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The absolute value of the integral {x=0..Pi/2} log(sin(x))^3 dx. The absolute value of m=3 of sqrt(Pi)/2*(d^m/da^m(gamma((a+1)/2)/gamma(a/2+1))) at a=0. - Seiichi Kirikami and Peter J. C. Moses, Oct 07 2011 REFERENCES I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products, 4th edition, 3.621.1 LINKS G. C. Greubel, Table of n, a(n) for n = 1..5000 FORMULA Equals A019675*(6*A002117 + A002388*A002162 + 4*A002162^3). EXAMPLE 6.041882909775093522150424130675995... MAPLE Pi/8*(6*Zeta(3)+Pi^2*log(2)+4*log(2)^3) ; evalf(%) ; # R. J. Mathar, Oct 08 2011 MATHEMATICA RealDigits[N[Pi/8 (6 Zeta[3] + Pi^2 Log[2] + 4 Log[2]^3), 150][[1]] Sqrt[Pi]/2*Derivative[3][Gamma[(#+1)/2]/Gamma[#/2+1]&][0] // RealDigits[#, 10, 105]& // First (* Jean-François Alcover, Mar 25 2013 *) PROG (PARI) Pi/8*(6*zeta(3)+Pi^2*log(2)+4*log(2)^3) \\ G. C. Greubel, Feb 12 2017 CROSSREFS Cf. A173623, A196877. Sequence in context: A202542 A019766 A094830 * A209835 A344973 A298528 Adjacent sequences:  A196875 A196876 A196877 * A196879 A196880 A196881 KEYWORD cons,nonn AUTHOR Seiichi Kirikami, Oct 07 2011 STATUS approved

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Last modified July 6 12:26 EDT 2022. Contains 355110 sequences. (Running on oeis4.)