%I A100554
%S A100554 5,7,6,6,7,4,0,4,7,4,6,8,5,8,1,1,7,4,1,3,4,0,5,0,7,9,4,7,5,0,0,0,0,4,9,
%T A100554 0,4,4,5,6,5,6,2,6,6,4,0,3,8,1,6,6,6,5,5,7,5,0,6,2,4,8,4,3,9,0,1,5,4,2,
%U A100554 4,7,9,1,8,3,1,0,0,2,1,7,4,3,5,6,5,5,5,1,7,5,9,3,9,5,4,9,1,8,7,6,5,1,7
%N A100554 Decimal expansion of the fractional part of Sum[Cos[(n + 1)*Pi]*Zeta[2*n], 
               {n, 1, Infinity}] = Zeta[2] - Zeta[4] + Zeta[6] - Zeta[8] + ..., 
               where Zeta is the Riemann zeta function.
%C A100554 For odd upper bounds, the sum converges to the given value p in (0,1) 
               with no fractional part function necessary. For even upper bounds, 
               the sum converges to p+1.
%C A100554 Decimal expansion of (psi(i)-psi(-i))/2/i-3/2 where psi is the digamma 
               function - Benoit Cloitre (benoit7848c(AT)orange.fr), Nov 28 2004
%e A100554 0.576674047468581174134050794750000490...
%t A100554 N[FractionalPart[Sum[Cos[(n + 1)*Pi]*Zeta[2*n], {n, 1, 500}]], 140] N[FractionalPart[Sum[Cos[(n 
               + 1)*Pi]*Zeta[2*n], {n, 1, 1000}]], 140]
%o A100554 (PARI) (psi(I)-psi(-I))/2/I-3/2
%Y A100554 Sequence in context: A144478 A059249 A114603 this_sequence A138306 A154802 
               A001620
%Y A100554 Adjacent sequences: A100551 A100552 A100553 this_sequence A100555 A100556 
               A100557
%K A100554 cons,nonn
%O A100554 0,1
%A A100554 Joseph Biberstine (jrbibers(AT)indiana.edu), Nov 27 2004