A363021 - OEIS

%I #13 May 19 2023 14:33:01

%S 9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,4,8,4,2,0,9,9,

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

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

%N Decimal expansion of Product_{k>=1} (1 - exp(-20*Pi*k)).

%F Equals exp(5*Pi/6) * Gamma(1/4) * (5^(1/4) - 1) * sqrt((sqrt(5) - 1)/5) / (2^(19/8) * Pi^(3/4)).

%e 0.999999999999999999999999999484209993745715964958151977112711625102369...

%t RealDigits[E^(5*Pi/6) * Gamma[1/4] * (5^(1/4) - 1) * Sqrt[(Sqrt[5] - 1)/5] / (2^(19/8)*Pi^(3/4)), 10, 120][[1]]

%t RealDigits[QPochhammer[E^(-20*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)), A363119 phi(exp(-14*Pi)), A363179 phi(exp(-15*Pi)), A292864 phi(exp(-16*Pi)), A363120 phi(exp(-18*Pi)).

%K nonn,cons

%O 0,1

%A _Vaclav Kotesovec_, May 13 2023