|
%I #35 May 02 2020 04:18:38
%S 1,0,0,0,2,4,6,0,8,6,5,5,3,3,0,8,0,4,8,2,9,8,6,3,7,9,9,8,0,4,7,7,3,9,
%T 6,7,0,9,6,0,4,1,6,0,8,8,4,5,8,0,0,3,4,0,4,5,3,3,0,4,0,9,5,2,1,3,3,2,
%U 5,2,0,1,9,6,8,1,9,4,0,9,1,3,0,4,9,0,4,2,8,0,8,5,5,1,9,0,0,6,9
%N Decimal expansion of zeta(12).
%D M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 811.
%H M. Abramowitz and I. A. Stegun, eds., <a href="http://www.convertit.com/Go/ConvertIt/Reference/AMS55.ASP">Handbook of Mathematical Functions</a>, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
%F zeta(12) = 2/3*2^12/(2^12 - 1)*( Sum_{n even} n^2*p(n)/(n^2 - 1)^13 ), where p(n) = 7*n^12 + 182*n^10 + 1001*n^8 + 1716*n^6 + 1001*n^4 + 182*n^2 + 7 is a row polynomial of A091043. - _Peter Bala_, Dec 05 2013
%F zeta(12) = Sum_{n >= 1} (A010052(n)/n^6) = Sum {n >= 1} ( (floor(sqrt(n))-floor(sqrt(n-1)))/n^6 ). - _Mikael Aaltonen_, Feb 20 2015
%F zeta(12) = 691/638512875*Pi^12 (see A002432). - _Rick L. Shepherd_, May 30 2016
%F zeta(12) = Product_{k>=1} 1/(1 - 1/prime(k)^12). - _Vaclav Kotesovec_, May 02 2020
%e 1.0002460865533080482986379980477396709604160884580034045330409521332520...
%t RealDigits[Zeta[12],10,120][[1]] (* _Harvey P. Dale_, Apr 30 2013 *)
%o (PARI) zeta(12) \\ _Michel Marcus_, Feb 20 2015
%Y Cf. A013662, A013664, A013666, A013668.
%K cons,nonn
%O 1,5
%A _N. J. A. Sloane_
|
