cp's OEIS Frontend

A013675 Decimal expansion of zeta(17).

%I A013675 #27 May 02 2020 04:21:55
%S A013675 1,0,0,0,0,0,7,6,3,7,1,9,7,6,3,7,8,9,9,7,6,2,2,7,3,6,0,0,2,9,3,5,6,3,
%T A013675 0,2,9,2,1,3,0,8,8,2,4,9,0,9,0,2,6,2,6,7,9,0,9,5,3,7,9,8,4,3,9,7,2,9,
%U A013675 3,5,6,4,3,2,9,0,2,8,2,4,5,9,3,4,2,0,8,1,7,3,8,6,3,6,9,1,6,6,7
%N A013675 Decimal expansion of zeta(17).
%H A013675 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, p. 811.
%F A013675 From _Peter Bala_, Dec 04 2013: (Start)
%F A013675 Definition: zeta(17) = sum {n >= 1} 1/n^17.
%F A013675 zeta(17) = 2^17/(2^17 - 1)*( sum {n even} n^11*p(n)*p(1/n)/(n^2 - 1)^18 ), where p(n) = n^8 + 36*n^6 + 126*n^4 + 84*n^2 + 9. Cf. A013663, A013667 and A013671.
%F A013675 (End)
%F A013675 zeta(17) = Sum_{n >= 1} (A010052(n)/n^(17/2)) = Sum_{n >= 1} ( (floor(sqrt(n)) - floor(sqrt(n-1)))/n^(17/2) ). - _Mikael Aaltonen_, Feb 23 2015
%F A013675 zeta(17) = Product_{k>=1} 1/(1 - 1/prime(k)^17). - _Vaclav Kotesovec_, May 02 2020
%e A013675 1.0000076371976378997622736002935630292130882490902626790953798439729356...
%t A013675 RealDigits[Zeta[17], 10, 75][[1]] (* _Vincenzo Librandi_, Feb 24 2015 *)
%o A013675 (PARI) zeta(17) \\ _Charles R Greathouse IV_, Dec 04 2013
%Y A013675 Cf. A013663, A013667, A013669, A013671, A013675, A013677, A010057.
%K A013675 cons,nonn
%O A013675 1,7
%A A013675 _N. J. A. Sloane_