A196878 Decimal expansion of (Pi/8)*(6*zeta(3)+Pi^2*log(2)+4*log(2)^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
Offset: 1
Examples
6.041882909775093522150424130675995...
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
- K. S. Kolbig, On the integral int_0^Pi/2 log^n cos x log^p sin x dx, Math. Comp. 40 (162) (1983) 565-570, r_{3,0}
Programs
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Maple
Pi/8*(6*Zeta(3)+Pi^2*log(2)+4*log(2)^3) ; evalf(%) ; # R. J. Mathar, Oct 08 2011
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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 *)
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PARI
Pi/8*(6*zeta(3)+Pi^2*log(2)+4*log(2)^3) \\ G. C. Greubel, Feb 12 2017
Comments