A363120 - OEIS

%I #10 May 19 2023 14:32:48

%S 9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,7,2,3,7,9,8,7,5,5,6,

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

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

%N Decimal expansion of Product_{k>=1} (1 - exp(-18*Pi*k)).

%H Mathematics Stack Exchange, <a href="https://math.stackexchange.com/questions/3101157/additional-values-of-dedekinds-eta-function-in-radical-form">Additional values of Dedekind's eta function in radical form</a>.

%F Equals exp(3*Pi/4) * Gamma(1/4) * (sqrt(6)*(2 + sqrt(3))^(1/6) - 3)^(1/3) / (6*Pi^(3/4)).

%e 0.999999999999999999999999723798755647764684512427204448244366188197087...

%t RealDigits[QPochhammer[E^(-18*Pi)], 10, 120][[1]]

%t RealDigits[E^(3*Pi/4) * Gamma[1/4] * (Sqrt[6]*(2 + Sqrt[3])^(1/6) - 3)^(1/3) / (6*Pi^(3/4)), 10, 120][[1]]

%Y Cf. A259148 phi(exp(-Pi)), A259149 phi(exp(-2*Pi)), A292888 phi(exp(-3*Pi)), A259150 phi(exp(-4*Pi)), A292905 phi(exp(-5*Pi)), A363018 phi(exp(-6*Pi)), A363117 phi(exp(-7*Pi)), A259151 phi(exp(-8*Pi)), A363118 phi(exp(-9*Pi)), A363019 phi(exp(-10*Pi)), A363081 phi(exp(-11*Pi)), A363020 phi(exp(-12*Pi)), A363178 phi(exp(-13*Pi)), A363119 phi(exp(-14*Pi)), A363179 phi(exp(-15*Pi)), A292864 phi(exp(-16*Pi)), A363021 phi(exp(-20*Pi)).

%K nonn,cons

%O 0,1

%A _Vaclav Kotesovec_, May 15 2023