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A013667
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Decimal expansion of zeta(9).
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18
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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, 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, 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
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OFFSET
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1,4
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REFERENCES
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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.
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LINKS
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Table of n, a(n) for n=1..99.
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
Simon Plouffe, Plouffe's Inverter, Zeta(9)=sum(1/n^9, n=1..infinity); to 20000 digits
Simon Plouffe, Zeta(9) or sum(1/n**9, n=1..infinity);
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FORMULA
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From Peter Bala, Dec 04 2013: (Start)
Definition: zeta(9) = sum {n >= 1} 1/n^9.
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)
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
zeta(9) = Product_{k>=1} 1/(1 - 1/prime(k)^9). - Vaclav Kotesovec, May 02 2020
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EXAMPLE
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1.0020083928260822...
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MAPLE
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evalf(Zeta(9)) ; # R. J. Mathar, Oct 16 2015
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MATHEMATICA
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RealDigits[Zeta[9], 10, 100][[1]] (* Harvey P. Dale, Aug 27 2014 *)
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CROSSREFS
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Cf. A013663, A013667, A013669, A013671, A013675, A013677.
Cf. A023876, A023877.
Sequence in context: A319568 A334411 A028698 * A091933 A058347 A058547
Adjacent sequences: A013664 A013665 A013666 * A013668 A013669 A013670
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KEYWORD
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nonn,cons
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AUTHOR
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N. J. A. Sloane.
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STATUS
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approved
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