cp's OEIS Frontend

A334450 Decimal expansion of Product_{k>=1} (1 - 1/A002144(k)^5).

%I A334450 #22 Jun 27 2020 11:51:41
%S A334450 9,9,9,6,7,6,5,2,7,0,7,9,6,2,6,6,6,2,0,1,8,2,4,6,1,8,0,8,7,3,0,8,3,7,
%T A334450 0,1,5,0,0,7,5,1,5,7,4,3,7,9,5,5,4,4,3,0,5,6,8,4,3,2,8,4,0,4,2,4,9,7,
%U A334450 5,9,8,1,9,2,1,2,1,9,1,3,2,9,9,7,0,4,0,0,3,0,2,9,1,9,3,0,4,4,5,3,7,5,2,8,3,9
%N A334450 Decimal expansion of Product_{k>=1} (1 - 1/A002144(k)^5).
%C A334450 In general, for s>0, Product_{k>=1} (1 + 1/A002144(k)^(2*s+1))/(1 - 1/A002144(k)^(2*s+1)) = Pi^(2*s+1) * A000364(s) * zeta(2*s+1) / ((2^(2*s+2) + 2) * (2*s)! * zeta(4*s+2)). - _Dimitris Valianatos_, May 01 2020
%C A334450 In general, for s>1, Product_{k>=1} (1 + 1/A002144(k)^s)/(1 - 1/A002144(k)^s) = (zeta(s, 1/4) - zeta(s, 3/4)) * zeta(s) / (2^s * (2^s + 1) * zeta(2*s)).
%D A334450 B. C. Berndt, Ramanujan's notebook part IV, Springer-Verlag, 1994, p. 64-65.
%H A334450 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 A334450 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 1 5 = 1/A334450).
%F A334450 A334449 / A334450 = 4725*zeta(5)/(16*Pi^5).
%F A334450 A334450 * A334452 = 32/(31*zeta(5)).
%e A334450 0.999676527079626662018246180873083701500751574379554430568432840424975981921219...
%Y A334450 Cf. A002144, A088539, A334446, A334450.
%K A334450 nonn,cons
%O A334450 0,1
%A A334450 _Vaclav Kotesovec_, Apr 30 2020
%E A334450 More digits from _Vaclav Kotesovec_, Jun 27 2020