login
Decimal expansion of 8*Pi^4/(21*zeta(3)).
0

%I #18 Jan 17 2020 03:35:15

%S 3,0,8,7,0,6,0,6,0,9,0,5,0,3,5,8,7,3,8,4,3,9,6,8,7,1,2,0,6,3,6,7,3,7,

%T 6,9,9,0,3,9,3,9,4,4,8,1,4,4,2,7,6,8,1,1,0,0,2,5,2,6,0,7,4,3,3,3,4,7,

%U 3,0,8,9,6,9,6,2,9,4,9,6,8,0,6,3,9,4,3,0,5,4,8,7,2,1,2,5,5,8,4,8,8,5,0,7,9

%N Decimal expansion of 8*Pi^4/(21*zeta(3)).

%C sum(k<N,r_3(k)^2) is asymptotic to 8*Pi^4*N^2/(21*zeta(3)) where r_3(n) is the number of representations of a positive integer n as a sum of 3 squares of integers.

%H S. K. K. Choi, A. V. Kumchev and R. Osburn, <a href="http://arXiv.org/abs/math.NT/0502007">On sums of three squares</a>, arXiv:math/0502007 [math.NT], 2005.

%H Steven R. Finch, <a href="http://arxiv.org/abs/2001.00578">Errata and Addenda to Mathematical Constants.</a> p. 18.

%F 30.870606090503587...

%t RealDigits[(8*Pi^4)/(21*Zeta[3]),10,120][[1]] (* _Harvey P. Dale_, Nov 29 2014 *)

%o (PARI) 8*Pi^4/21/zeta(3)

%Y Cf. A005875.

%K cons,nonn

%O 2,1

%A _Benoit Cloitre_, May 24 2005