A363119 - OEIS

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

%S 9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,2,0,7,9,8,9,3,0,4,9,2,0,1,8,8,

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

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

%N Decimal expansion of Product_{k>=1} (1 - exp(-14*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(7*Pi/12) * Gamma(1/4) * sqrt(sqrt(5 - sqrt(7)) - sqrt(3*sqrt(7) - 7)) / (2^(13/8) * 7^(7/16) * Pi^(3/4)).

%e 0.999999999999999999920798930492018877357821248361115796849980384110811...

%t RealDigits[E^(7*Pi/12) * Gamma[1/4] * Sqrt[Sqrt[5 - Sqrt[7]] - Sqrt[3*Sqrt[7] - 7]] / (2^(13/8) * 7^(7/16) * Pi^(3/4)), 10, 120][[1]]

%t RealDigits[QPochhammer[E^(-14*Pi)], 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)), A363179 phi(exp(-15*Pi)), A292864 phi(exp(-16*Pi)), A363120 phi(exp(-18*Pi)), A363021 phi(exp(-20*Pi)).

%K nonn,cons

%O 0,1

%A _Vaclav Kotesovec_, May 15 2023