A363118 Decimal expansion of Product_{k>=1} (1 - exp(-9*Pi*k)).

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

Offset

0,1

Links

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

Formula

Equals exp(3*Pi/8) * Gamma(1/4) * ((3*(6 + 7*sqrt(3) + 3*sqrt(14*sqrt(3) - 15)))^(1/3) - 3)^(1/3) / (3 * 2^(7/8) * Pi^(3/4)).

Example

0.999999999999474451482399078943233394928797164400527513438819873918260...

Mathematica

RealDigits[E^(3*Pi/8) * Gamma[1/4] * ((3*(6 + 7*Sqrt[3] + 3*Sqrt[14*Sqrt[3] - 15]))^(1/3) - 3)^(1/3) / (3 * 2^(7/8) * Pi^(3/4)), 10, 120][[1]]
RealDigits[QPochhammer[E^(-9*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)), 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: A270172 A332550 A137577 * A363019 A363081 A363020

Adjacent sequences: A363115 A363116 A363117 * A363119 A363120 A363121

Keyword

nonn,cons

Author

Vaclav Kotesovec, May 15 2023

Status

approved