OFFSET
1,2
LINKS
J. M. Borwein, A. Straub, J. Wan, and W. Zudilin, Densities of short uniform random walks, arXiv:1103.2995 [math.CA], (11-August-2011)
Steven R. Finch, Mathematical Constants II, Encyclopedia of Mathematics and Its Applications, Cambridge University Press, Cambridge, 2018, p. 464.
FORMULA
Integral_(0..3) x*p(x) dx, where p(x) = 2*sqrt(3)/Pi*x/(3+x^2) * 2F1(1/3, 2/3; 1; x^2*(9-x^2)^2/(3+x^2)^3), 2F1 being the hypergeometric function.
Re(3F2(-1/2, -1/2, 1/2; 1, 1; 4)).
(3*2^(1/3))/(16*Pi^4)*Gamma(1/3)^6 + (27*2^(2/3))/(4*Pi^4)*Gamma(2/3)^6.
EXAMPLE
1.5745972375518936574946921830765...
MATHEMATICA
(3*2^(1/3))/(16*Pi^4)*Gamma[1/3]^6 + (27*2^(2/3))/(4*Pi^4)*Gamma[2/3]^6 //
RealDigits[#, 10, 100]& // First (* updated May 20 2015 *)
CROSSREFS
KEYWORD
AUTHOR
Jean-François Alcover, Aug 04 2014
EXTENSIONS
More digits from Jean-François Alcover, May 20 2015
STATUS
approved