|
%I #24 Sep 08 2022 08:46:04
%S 1,8,3,1,9,3,1,1,8,8,3,5,4,4,3,8,0,3,0,1,0,9,2,0,7,0,2,9,8,6,4,7,6,8,
%T 2,2,1,5,4,8,2,9,8,7,4,8,5,6,3,3,4,4,2,6,8,5,3,2,9,9,6,2,3,9,2,4,3,5,
%U 2,6,0,3,9,5,5,2,5,0,9,5,3,8,9,5,8,7,1,3,0,2,5,8,5,2,2,3,0,2,1,2
%N Decimal expansion of two times the Catalan constant.
%D I.S. Gradshteyn and I.M. Ryzhik, Table of integrals, series and products, 5th edition, Academic Press, 1994, eq. (3.521.2).
%H G. C. Greubel, <a href="/A221209/b221209.txt">Table of n, a(n) for n = 1..10000</a>
%F Equals Integral_{x=0..oo} x/cosh(x) dx.
%F Equals 2*A006752.
%F From _Amiram Eldar_, Aug 20 2020: (Start)
%F Equals Integral_{x=0..Pi/2} x/sin(x) dx.
%F Equals 1 + Integral_{x=0..oo} x * exp(-x) * tanh(x) dx. (End)
%e 1.83193118835443803010920702986476822154...
%p evalf(2*Catalan) ;
%t RealDigits[2 Catalan, 10, 100][[1]] (* _Bruno Berselli_, Feb 21 2013 *)
%o (PARI) default(realprecision, 100); 2*Catalan \\ _G. C. Greubel_, Aug 25 2018
%o (Magma) SetDefaultRealField(RealField(100)); R:=RealField(); 2*Catalan(R); // _G. C. Greubel_, Aug 25 2018
%Y Cf. A006752.
%K nonn,cons,easy
%O 1,2
%A _R. J. Mathar_, Feb 21 2013
|
