A013667 - OEIS

%I #34 May 02 2020 04:09:22

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

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

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

%N Decimal expansion of zeta(9).

%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].

%H Simon Plouffe, Plouffe's Inverter, <a href="http://www.plouffe.fr/simon/constants/zeta9.txt">Zeta(9)=sum(1/n^9, n=1..infinity); to 20000 digits</a>

%H Simon Plouffe, <a href="http://www.worldwideschool.org/library/books/sci/math/MiscellaneousMathematicalConstants/chap101.html">Zeta(9) or sum(1/n**9, n=1..infinity);</a>

%F From _Peter Bala_, Dec 04 2013: (Start)

%F Definition: zeta(9) = sum {n >= 1} 1/n^9.

%F zeta(9) = 2^9/(2^9 - 1)*( sum {n even} n^7*p(n)*p(1/n)/(n^2 - 1)^10 ), where p(n) = n^4 + 10*n^2 + 5. See A013663, A013671 and A013675. (End)

%F zeta(9) = Sum_{n >= 1} (A010052(n)/n^(9/2)) = Sum_{n >= 1} ( (floor(sqrt(n))-floor(sqrt(n-1)))/n^(9/2) ). - _Mikael Aaltonen_, Feb 22 2015

%F zeta(9) = Product_{k>=1} 1/(1 - 1/prime(k)^9). - _Vaclav Kotesovec_, May 02 2020

%e 1.0020083928260822...

%p evalf(Zeta(9)) ; # _R. J. Mathar_, Oct 16 2015

%t RealDigits[Zeta[9],10,100][[1]] (* _Harvey P. Dale_, Aug 27 2014 *)

%Y Cf. A013663, A013667, A013669, A013671, A013675, A013677.

%Y Cf. A023876, A023877.

%K nonn,cons

%O 1,4

%A _N. J. A. Sloane_.