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Decimal expansion of Product_{k>=1} (1 - 1/A002145(k)^5).
6

%I #22 Jun 27 2020 11:50:59

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

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

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

%N Decimal expansion of Product_{k>=1} (1 - 1/A002145(k)^5).

%C In general, for s>0, Product_{k>=1} (1 + 1/A002145(k)^(2*s+1))/(1 - 1/A002145(k)^(2*s+1)) = (2*s)! * (2^(2*s + 2) - 2) * zeta(2*s+1) / (Pi^(2*s+1) * A000364(s)). - _Dimitris Valianatos_, May 01 2020

%C In general, for s>1, Product_{k>=1} (1 + 1/A002145(k)^s)/(1 - 1/A002145(k)^s) = 2^s * (2^s - 1) * zeta(s) / (zeta(s, 1/4) - zeta(s, 3/4)).

%D B. C. Berndt, Ramanujan's notebook part IV, Springer-Verlag, 1994, p. 64-65.

%H Ph. Flajolet and I. Vardi, <a href="http://algo.inria.fr/flajolet/Publications/landau.ps">Zeta function expansions of some classical constants</a>, Feb 18 1996, p. 7-8.

%H R. J. Mathar, <a href="http://arxiv.org/abs/1008.2547">Table of Dirichlet L-series and Prime Zeta Modulo Functions for Small Moduli</a>, arXiv:1008.2547 [math.NT], 2010-2015, p. 26 (case 4 3 5 = 1/A334452).

%F A334451 / A334452 = 1488*zeta(5)/(5*Pi^5).

%F A334450 * A334452 = 32/(31*zeta(5)).

%e 0.99581872986808059594338516164316597187434727318491056639835771469803963967031...

%Y Cf. A002145, A243379, A334427, A334448.

%K nonn,cons

%O 0,1

%A _Vaclav Kotesovec_, Apr 30 2020

%E More digits from _Vaclav Kotesovec_, Jun 27 2020