OFFSET
1,2
COMMENTS
The computation of this integral was mentioned as a challenge by Robert Israel on the newsgroup sci.math (Dec 22 2010), a closed form solution being given by Valeri Astanoff.
LINKS
The Math Forum at Drexel - Valeri Astanoff Re: Nice Integral, Dec 22, 2010.
EXAMPLE
1.9754169..
MATHEMATICA
RealDigits[N[(3/8)*(Pi^2*Log[4] - 7*Zeta[3]) , 110]][[1]]
(* or as a numerical check : *)
RealDigits[NIntegrate[ArcTan[1/x]^3, {x, 0, Infinity}, WorkingPrecision -> 110]][[1]] (* Jean-François Alcover, Mar 23 2011 *)
RealDigits[ N[ Integrate[ ArcTan[1/x]^3, {x, 0, Infinity}], 110]][[1]] (* Jean-François Alcover, Oct 19 2012, since version 6.0 *)
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Jean-François Alcover, Mar 23 2011
STATUS
approved