A013675 Decimal expansion of zeta(17).
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, 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, 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
Offset: 1
Examples
1.0000076371976378997622736002935630292130882490902626790953798439729356...
Links
- M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972, p. 811.
Programs
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Mathematica
RealDigits[Zeta[17], 10, 75][[1]] (* Vincenzo Librandi, Feb 24 2015 *)
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PARI
zeta(17) \\ Charles R Greathouse IV, Dec 04 2013
Formula
From Peter Bala, Dec 04 2013: (Start)
Definition: zeta(17) = sum {n >= 1} 1/n^17.
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.
(End)
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
zeta(17) = Product_{k>=1} 1/(1 - 1/prime(k)^17). - Vaclav Kotesovec, May 02 2020