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 A013667 Decimal expansion of zeta(9). 58
 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 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 REFERENCES 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. LINKS 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); FORMULA 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 EXAMPLE 1.0020083928260822... MAPLE evalf(Zeta(9)) ; # R. J. Mathar, Oct 16 2015 MATHEMATICA RealDigits[Zeta[9], 10, 100][[1]] (* Harvey P. Dale, Aug 27 2014 *) CROSSREFS 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 KEYWORD nonn,cons AUTHOR N. J. A. Sloane. STATUS approved

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Last modified August 3 23:57 EDT 2024. Contains 374905 sequences. (Running on oeis4.)