A013669 Decimal expansion of zeta(11).
1, 0, 0, 0, 4, 9, 4, 1, 8, 8, 6, 0, 4, 1, 1, 9, 4, 6, 4, 5, 5, 8, 7, 0, 2, 2, 8, 2, 5, 2, 6, 4, 6, 9, 9, 3, 6, 4, 6, 8, 6, 0, 6, 4, 3, 5, 7, 5, 8, 2, 0, 8, 6, 1, 7, 1, 1, 9, 1, 4, 1, 4, 3, 6, 1, 0, 0, 0, 5, 4, 0, 5, 9, 7, 9, 8, 2, 1, 9, 8, 1, 4, 7, 0, 2, 5, 9, 1, 8, 4, 3, 0, 2, 3, 5, 6, 0, 6, 2
Offset: 1
Examples
1.0004941886041194645587022825264699364686064357582...
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
- 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].
- Jonathan Borwein and David Bradley, Empirically determined Apéry-like formulae for zeta(4n+3), Experimental Mathematics, Vol. 6, No. 3 (1997), pp. 181-194; arXiv preprint, arXiv:math/0505124 [math.CA], 2005.
Programs
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Maple
evalf(Zeta(11), 150) ; # R. J. Mathar, Oct 16 2015
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Mathematica
RealDigits[Zeta[11], 10, 120][[1]] (* Amiram Eldar, Jun 11 2023 *)
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PARI
zeta(11) \\ Charles R Greathouse IV, Apr 25 2016
Formula
zeta(11) = Sum_{n >= 1} (A010052(n)/n^(11/2)) = Sum_{n >= 1} ( (floor(sqrt(n))-floor(sqrt(n-1)))/n^(11/2) ). - Mikael Aaltonen, Feb 22 2015
zeta(11) = Product_{k>=1} 1/(1 - 1/prime(k)^11). - Vaclav Kotesovec, May 02 2020
Extensions
a(99) corrected by Sean A. Irvine, Sep 05 2018