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%I #9 May 19 2023 14:31:36
%S 9,9,9,9,9,9,9,9,9,9,9,9,4,7,4,4,5,1,4,8,2,3,9,9,0,7,8,9,4,3,2,3,3,3,
%T 9,4,9,2,8,7,9,7,1,6,4,4,0,0,5,2,7,5,1,3,4,3,8,8,1,9,8,7,3,9,1,8,2,6,
%U 0,6,6,0,2,4,0,5,6,1,9,2,1,1,3,2,7,4,3,6,9,7,0,9,0,8,3,8,4,0,0,8,2,7,2,0,3,0
%N Decimal expansion of Product_{k>=1} (1 - exp(-9*Pi*k)).
%F Equals exp(3*Pi/8) * Gamma(1/4) * ((3*(6 + 7*sqrt(3) + 3*sqrt(14*sqrt(3) - 15)))^(1/3) - 3)^(1/3) / (3 * 2^(7/8) * Pi^(3/4)).
%e 0.999999999999474451482399078943233394928797164400527513438819873918260...
%t RealDigits[E^(3*Pi/8) * Gamma[1/4] * ((3*(6 + 7*Sqrt[3] + 3*Sqrt[14*Sqrt[3] - 15]))^(1/3) - 3)^(1/3) / (3 * 2^(7/8) * Pi^(3/4)), 10, 120][[1]]
%t RealDigits[QPochhammer[E^(-9*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)), 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)), A363021 phi(exp(-20*Pi)).
%K nonn,cons
%O 0,1
%A _Vaclav Kotesovec_, May 15 2023