Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #16 May 19 2023 14:31:48
%S 9,9,9,9,9,9,9,9,9,9,9,9,9,7,7,2,8,8,9,8,9,3,1,6,7,5,8,5,4,5,8,2,3,2,
%T 0,0,9,9,3,3,2,5,0,2,9,4,8,2,7,0,7,0,6,7,4,1,3,2,0,5,4,5,3,3,6,2,9,9,
%U 5,3,9,3,6,4,0,1,3,8,4,1,9,7,2,4,3,0,5,3,4,8,2,3,7,3,4,5,6,9,4,5,3,8,7,7,7,0
%N Decimal expansion of Product_{k>=1} (1 - exp(-10*Pi*k)).
%F Equals exp(5*Pi/12) * Gamma(5/4) * sqrt(2*(sqrt(5) - 1)/5) / Pi^(3/4).
%F Equals A292905 * A292904.
%e 0.999999999999977288989316758545823200993325029482707067413205453362995...
%t RealDigits[E^(5*Pi/12)*Gamma[5/4]*Sqrt[2*(Sqrt[5] - 1)/5]/Pi^(3/4), 10, 120][[1]]
%t RealDigits[QPochhammer[E^(-10*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)), 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 13 2023