%I A113319
%S A113319 2,0,7,6,6,7,4,0,4,7,4,6,8,5,8,1,1,7,4,1,3,4,0,5,0,7,9,4,7,5,0,0,0,0,4,
%T A113319 9,0,4,4,5,6,5,6,2,6,6,4,0,3,8,1,6,6,6,5,5,7,5,0,6,2,4,8,4,3,9,0,1,5,4,
%U A113319 2,4,7,9,1,8,3,1,0,0,2,1,7,4,3,5,6,5,5,5,1,7,5,9,3,9,5,4,9,1,8,7,6,5,1
%N A113319 Decimal expansion of sum(k>=0,1/(k^2+1)).
%C A113319 Known to be transcendental. After n=2 it is the same as A100554(n).
%D A113319 Michel Waldschmidt, Elliptic functions and transcendance, dec. 2005, 
               to appear
%F A113319 sum(k>=0, 1/(k^2+1))=1/2+Pi/2/tanh(Pi)=2.0766740474685811741...
%o A113319 (PARI) 1/2+Pi/2/tanh(Pi)
%Y A113319 Sequence in context: A011343 A021486 A104540 this_sequence A021832 A160509 
               A049006
%Y A113319 Adjacent sequences: A113316 A113317 A113318 this_sequence A113320 A113321 
               A113322
%K A113319 cons,nonn
%O A113319 0,1
%A A113319 Benoit Cloitre (benoit7848c(AT)orange.fr), Jan 07 2006