|
%I #16 Apr 12 2022 03:41:14
%S 6,3,9,5,1,0,3,5,1,8,7,0,3,1,1,0,0,1,9,6,2,6,9,3,0,8,5,4,2,7,3,2,3,6,
%T 7,9,8,7,5,9,9,4,6,2,5,1,8,4,7,2,8,2,9,5,1,5,8,5,6,2,3,0,8,0,2,9,2,0,
%U 5,1,6,6,3,5,6,2,5,0,3,0,5,1,8,4,8,9,7,8,9,5,4,7,7,4,2,7,3,1,6,0,3,5
%N Decimal expansion of -Catalan + (Pi*arcsinh(1))/2 + HypergeometricPFQ[{1/2, 1, 1}, {3/2, 3/2}, 1/9]/6.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/RadialIntegrals.html">Radial Integrals</a>.
%F Equals Integral_{x=0..1, y=0..1} 1/(x^2 + y^2 + 1) dy dx.
%F Equals Integral_{x=0..1} arccot(sqrt(x^2+1))/sqrt(x^2+1) dx. - _Amiram Eldar_, Apr 12 2022
%e 0.63951035187031100196269308542732367987599462518472...
%t RealDigits[-Catalan + (Pi*ArcSinh[1])/2 + HypergeometricPFQ[{1/2, 1, 1}, {3/2, 3/2}, 1/9]/6, 10, 100][[1]] (* _Amiram Eldar_, Apr 12 2022 *)
%Y Cf. A000796, A006752, A091648, A093753.
%K nonn,cons
%O 0,1
%A _Eric W. Weisstein_, Apr 15 2004
%E Keyword:cons added by _R. J. Mathar_, Apr 01 2010
|
