cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A363019 Decimal expansion of Product_{k>=1} (1 - exp(-10*Pi*k)).

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%I A363019 #16 May 19 2023 14:31:48
%S A363019 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 A363019 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 A363019 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 A363019 Decimal expansion of Product_{k>=1} (1 - exp(-10*Pi*k)).
%F A363019 Equals exp(5*Pi/12) * Gamma(5/4) * sqrt(2*(sqrt(5) - 1)/5) / Pi^(3/4).
%F A363019 Equals A292905 * A292904.
%e A363019 0.999999999999977288989316758545823200993325029482707067413205453362995...
%t A363019 RealDigits[E^(5*Pi/12)*Gamma[5/4]*Sqrt[2*(Sqrt[5] - 1)/5]/Pi^(3/4), 10, 120][[1]]
%t A363019 RealDigits[QPochhammer[E^(-10*Pi)], 10, 120][[1]]
%Y A363019 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 A363019 nonn,cons
%O A363019 0,1
%A A363019 _Vaclav Kotesovec_, May 13 2023