A363018 Decimal expansion of Product_{k>=1} (1 - exp(-6*Pi*k)).

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

Offset

0,1

Links

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

Formula

Equals exp(Pi/4) * Gamma(1/4) * (2 - sqrt(3))^(1/12) / (2 * 3^(3/8) * Pi^(3/4)).

Equals A292888 * A292887.

Example

0.999999993487587821508587441627061243108330508136097236620870239066239...

Mathematica

RealDigits[E^(Pi/4)*Gamma[1/4]*(2 - Sqrt[3])^(1/12)/(2*3^(3/8)*Pi^(3/4)), 10, 120][[1]]
RealDigits[QPochhammer[E^(-6*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)), 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)), A363120 phi(exp(-18*Pi)), A363021 phi(exp(-20*Pi)).

Sequence in context: A277535 A292905 A361352 * A269351 A363117 A116667

Adjacent sequences: A363015 A363016 A363017 * A363019 A363020 A363021

Keyword

nonn,cons

Author

Vaclav Kotesovec, May 13 2023

Status

approved