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A013665 Decimal expansion of zeta(7). 11

%I

%S 1,0,0,8,3,4,9,2,7,7,3,8,1,9,2,2,8,2,6,8,3,9,7,9,7,5,4,9,8,4,9,7,9,6,

%T 7,5,9,5,9,9,8,6,3,5,6,0,5,6,5,2,3,8,7,0,6,4,1,7,2,8,3,1,3,6,5,7,1,6,

%U 0,1,4,7,8,3,1,7,3,5,5,7,3,5,3,4,6,0,9,6,9,6,8,9,1,3,8,5,1,3,2

%N Decimal expansion of zeta(7).

%D 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.

%H M. Abramowitz and I. A. Stegun, eds., <a href="http://www.convertit.com/Go/ConvertIt/Reference/AMS55.ASP">Handbook of Mathematical Functions</a>, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].

%H Jakob Ablinger, <a href="https://arxiv.org/abs/1908.06631">Proving two conjectural series for zeta(7) and discovering more series for zeta(7)</a>, arXiv:1908.06631 [math.CO], 2019.

%H J. Borwein and D. Bradley, <a href="http://arXiv.org/abs/math.CA/0505124">Empirically determined Apéry-like formulas for zeta(4n+3)</a>, arXiv:math/0505124 [math.CA], 2005.

%H Michael J. Dancs, Tian-Xiao He, <a href="http://dx.doi.org/10.1016/j.jnt.2005.09.005">An Euler-type formula for zeta(2k+1)</a>, Journal of Number Theory, Volume 118, Issue 2, June 2006, Pages 192-199.

%H Simon Plouffe, Plouffe's Inverter, <a href="http://www.plouffe.fr/simon/constants/zeta7.txt">Zeta(7) to 50000 digits</a>

%H Simon Plouffe, <a href="http://www.worldwideschool.org/library/books/sci/math/MiscellaneousMathematicalConstants/chap100.html">Zeta(7) to 512 places:sum(1/n^7, n=1..infinity)</a>

%F zeta(7) = Sum_{n >= 1} (A010052(n)/n^(7/2)) = Sum_{n >= 1} ( (floor(sqrt(n))-floor(sqrt(n-1)))/n^(7/2) ). - _Mikael Aaltonen_, Feb 22 2015

%e 1.0083492773819228268397975498497967595998635605652387064172831365716014...

%t RealDigits[Zeta[7],10,120][[1]] (* _Harvey P. Dale_, Oct 23 2012 *)

%o (PARI) zeta(7) \\ _Michel Marcus_, Apr 17 2016

%Y Cf. A023874, A023875, A248884.

%K cons,nonn

%O 1,4

%A _N. J. A. Sloane_.

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Last modified October 20 07:23 EDT 2019. Contains 328252 sequences. (Running on oeis4.)