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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-Fran├žois 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 A298528 A021947

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 January 22 19:44 EST 2020. Contains 331153 sequences. (Running on oeis4.)