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A013676 Decimal expansion of zeta(18). 6

%I #24 May 02 2020 04:22:31

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

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

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

%N Decimal expansion of zeta(18).

%D Milton Abramowitz and Irene A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 811.

%H Milton Abramowitz and Irene 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(18) = Sum_{n >= 1} (A010052(n)/n^9) = Sum_{n >= 1} ( (floor(sqrt(n))-floor(sqrt(n-1)))/n^9 ). - _Mikael Aaltonen_, Mar 06 2015

%F zeta(18) = 43867*Pi^18/38979295480125 = A046988(9)*Pi^18/A002432(9). - _Alonso del Arte_, Feb 12 2016

%F zeta(18) = Product_{k>=1} 1/(1 - 1/prime(k)^18). - _Vaclav Kotesovec_, May 02 2020

%e 1.0000038172932649998398564616446219397...

%t RealDigits[Zeta[18], 10, 100][[1]] (* _Alonso del Arte_, Feb 07 2016 *)

%o (PARI) zeta(18) \\ _Michel Marcus_, Feb 12 2016

%K cons,nonn

%O 1,7

%A _N. J. A. Sloane_

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Last modified March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)