|
%I #6 Sep 25 2017 11:26:42
%S 9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,8,5,2,0,9,6,5,3,8,4,0,3,8,
%T 2,1,4,3,4,7,4,5,7,7,5,5,7,0,0,4,9,4,1,6,3,1,3,1,4,3,4,3,3,1,1,3,7,1,
%U 7,6,6,7,2,0,2,2,1,4,4,9,4,7,6,1,6,8,9,7,0,9,0,9,5,2,0,5,8,6,9,3,8,7,6,7,4,9
%N Decimal expansion of Product_{k>=1} (1 - exp(-16*Pi*k)).
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/DedekindEtaFunction.html">Dedekind Eta Function</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/q-PochhammerSymbol.html">q-Pochhammer Symbol</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Dedekind_eta_function">Dedekind eta function</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Euler_function">Euler function</a>
%F Equals (3*sqrt(22*sqrt(2) - 24) - 8)^(1/8) * exp(2*Pi/3) * Gamma(1/4) / (2^(19/8) * Pi^(3/4)).
%e 0.999999999999999999999852096538403821434745775570049416313143433113717...
%t RealDigits[(3*Sqrt[-24 + 22*Sqrt[2]] - 8)^(1/8) * E^(2*Pi/3) * Gamma[1/4] / (2^(19/8)*Pi^(3/4)), 10, 120][[1]]
%t RealDigits[QPochhammer[E^(-16*Pi)], 10, 120][[1]]
%Y Cf. A259147, A259148, A259149, A259150, A259151, A292862, A292863.
%K nonn,cons
%O 0,1
%A _Vaclav Kotesovec_, Sep 25 2017
|
