# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a334447 Showing 1-1 of 1 %I A334447 #13 Jun 27 2020 11:52:37 %S A334447 1,0,1,2,8,4,9,7,3,7,5,0,3,6,5,8,2,4,1,0,5,3,7,3,8,8,0,9,6,3,0,1,1,2, %T A334447 0,3,9,6,8,4,5,0,4,2,1,6,5,5,3,8,6,9,4,5,0,9,2,2,2,1,4,4,1,8,1,9,1,3, %U A334447 4,1,5,6,6,9,0,0,5,5,2,5,7,1,6,6,4,2,4,8,6,1,2,7,5,4,1,3,0,2,9,9,9,3,4,4,9 %N A334447 Decimal expansion of Product_{k>=1} (1 + 1/A002145(k)^4). %C A334447 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)) = 1 / (2 * (-1)^s * PolyGamma(s-1, 1/4) / (2^s * (2^s - 1) * Gamma(s) * zeta(s)) - 1). %D A334447 B. C. Berndt, Ramanujan's notebook part IV, Springer-Verlag, 1994, p. 64-65. %H A334447 Ph. Flajolet and I. Vardi, Zeta function expansions of some classical constants, Feb 18 1996, p. 7-8. %F A334447 A334447 / A334448 = 1/(PolyGamma(3, 1/4)/(8*Pi^4) - 1). %F A334447 A334445 * A334447 = 1680 / (17*Pi^4). %e A334447 1.01284973750365824105373880963011203968450421655386945092221... %Y A334447 Cf. A002145, A243381, A334426, A334451. %K A334447 nonn,cons %O A334447 1,4 %A A334447 _Vaclav Kotesovec_, Apr 30 2020 %E A334447 More digits from _Vaclav Kotesovec_, Jun 27 2020 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE