cp's OEIS Frontend

A013669 Decimal expansion of zeta(11).

%I A013669 #37 Jun 11 2023 02:56:14
%S A013669 1,0,0,0,4,9,4,1,8,8,6,0,4,1,1,9,4,6,4,5,5,8,7,0,2,2,8,2,5,2,6,4,6,9,
%T A013669 9,3,6,4,6,8,6,0,6,4,3,5,7,5,8,2,0,8,6,1,7,1,1,9,1,4,1,4,3,6,1,0,0,0,
%U A013669 5,4,0,5,9,7,9,8,2,1,9,8,1,4,7,0,2,5,9,1,8,4,3,0,2,3,5,6,0,6,2
%N A013669 Decimal expansion of zeta(11).
%D A013669 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 A013669 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].
%H A013669 Jonathan Borwein and David Bradley, <a href="https://doi.org/10.1080/10586458.1997.10504608">Empirically determined Apéry-like formulae for zeta(4n+3)</a>, Experimental Mathematics, Vol. 6, No. 3 (1997), pp. 181-194; <a href="http://arXiv.org/abs/math.CA/0505124">arXiv preprint</a>, arXiv:math/0505124 [math.CA], 2005.
%F A013669 zeta(11) = Sum_{n >= 1} (A010052(n)/n^(11/2)) = Sum_{n >= 1} ( (floor(sqrt(n))-floor(sqrt(n-1)))/n^(11/2) ). - _Mikael Aaltonen_, Feb 22 2015
%F A013669 zeta(11) = Product_{k>=1} 1/(1 - 1/prime(k)^11). - _Vaclav Kotesovec_, May 02 2020
%e A013669 1.0004941886041194645587022825264699364686064357582...
%p A013669 evalf(Zeta(11), 150) ; # _R. J. Mathar_, Oct 16 2015
%t A013669 RealDigits[Zeta[11], 10, 120][[1]] (* _Amiram Eldar_, Jun 11 2023 *)
%o A013669 (PARI) zeta(11) \\ _Charles R Greathouse IV_, Apr 25 2016
%Y A013669 Cf. A010052, A013663, A013667, A013669, A013671, A013675, A013677, A023878.
%K A013669 cons,nonn
%O A013669 1,5
%A A013669 _N. J. A. Sloane_
%E A013669 a(99) corrected by _Sean A. Irvine_, Sep 05 2018