A013667 Decimal expansion of zeta(9).

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

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