A363120 Decimal expansion of Product_{k>=1} (1 - exp(-18*Pi*k)).

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

Offset

0,1

Links

Table of n, a(n) for n=0..105.

Mathematics Stack Exchange, Additional values of Dedekind's eta function in radical form.

Formula

Equals exp(3*Pi/4) * Gamma(1/4) * (sqrt(6)*(2 + sqrt(3))^(1/6) - 3)^(1/3) / (6*Pi^(3/4)).

Example

0.999999999999999999999999723798755647764684512427204448244366188197087...

Mathematica

RealDigits[QPochhammer[E^(-18*Pi)], 10, 120][[1]]
RealDigits[E^(3*Pi/4) * Gamma[1/4] * (Sqrt[6]*(2 + Sqrt[3])^(1/6) - 3)^(1/3) / (6*Pi^(3/4)), 10, 120][[1]]

Crossrefs

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)), A363021 phi(exp(-20*Pi)).

Sequence in context: A363119 A363179 A292864 * A363021 A099646 A181693

Adjacent sequences: A363117 A363118 A363119 * A363121 A363122 A363123

Keyword

nonn,cons

Author

Vaclav Kotesovec, May 15 2023

Status

approved