A363020 Decimal expansion of Product_{k>=1} (1 - exp(-12*Pi*k)).

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

Offset

0,1

Links

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

Formula

Equals exp(Pi/2) * Gamma(1/4) * (7 + 28*sqrt(3) - 2*sqrt(6*(469*sqrt(3) - 684)))^(1/24) / (2^(11/8) * 3^(3/8) * Pi^(3/4)).

Example

0.999999999999999957588488169839222761089020220559669362727608370525037...

Mathematica

RealDigits[E^(Pi/2) * Gamma[1/4] * (7 + 28*Sqrt[3] - 2*Sqrt[6*(-684 + 469*Sqrt[3])])^(1/24) / (2^(11/8)*3^(3/8)*Pi^(3/4)), 10, 120][[1]]
RealDigits[QPochhammer[E^(-12*Pi)], 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)), 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)).

Sequence in context: A363118 A363019 A363081 * A363178 A363119 A363179

Adjacent sequences: A363017 A363018 A363019 * A363021 A363022 A363023

Keyword

nonn,cons

Author

Vaclav Kotesovec, May 13 2023

Status

approved