cp's OEIS Frontend

A334448 Decimal expansion of Product_{k>=1} (1 - 1/A002145(k)^4).

%I A334448 #18 Jun 27 2020 11:52:19
%S A334448 9,8,7,1,6,2,6,2,5,4,2,2,2,2,6,8,5,6,4,8,2,7,0,1,2,6,4,5,7,7,3,7,0,8,
%T A334448 2,7,7,2,4,0,3,2,7,9,7,2,9,2,8,2,4,1,4,7,4,3,4,8,3,2,6,5,0,8,5,5,7,3,
%U A334448 0,8,9,4,7,5,6,6,7,0,0,1,8,8,9,0,8,4,1,5,0,4,9,9,8,9,0,7,3,3,4,7,7,0,3,5,3,6
%N A334448 Decimal expansion of Product_{k>=1} (1 - 1/A002145(k)^4).
%C A334448 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 A334448 B. C. Berndt, Ramanujan's notebook part IV, Springer-Verlag, 1994, p. 64-65.
%H A334448 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 A334448 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 4 = 1/A334448).
%F A334448 A334447 / A334448 = 1/(PolyGamma(3, 1/4)/(8*Pi^4) - 1).
%F A334448 A334446 * A334448 = 96/Pi^4.
%e A334448 0.98716262542222685648270126457737082772403279729282414743483...
%Y A334448 Cf. A002145, A243379, A334427, A334452.
%K A334448 nonn,cons
%O A334448 0,1
%A A334448 _Vaclav Kotesovec_, Apr 30 2020
%E A334448 More digits from _Vaclav Kotesovec_, Jun 27 2020