A363119 Decimal expansion of Product_{k>=1} (1 - exp(-14*Pi*k)).

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

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(7*Pi/12) * Gamma(1/4) * sqrt(sqrt(5 - sqrt(7)) - sqrt(3*sqrt(7) - 7)) / (2^(13/8) * 7^(7/16) * Pi^(3/4)).

Example

0.999999999999999999920798930492018877357821248361115796849980384110811...

Mathematica

RealDigits[E^(7*Pi/12) * Gamma[1/4] * Sqrt[Sqrt[5 - Sqrt[7]] - Sqrt[3*Sqrt[7] - 7]] / (2^(13/8) * 7^(7/16) * Pi^(3/4)), 10, 120][[1]]
RealDigits[QPochhammer[E^(-14*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)), A363020 phi(exp(-12*Pi)), A363178 phi(exp(-13*Pi)), A363179 phi(exp(-15*Pi)), A292864 phi(exp(-16*Pi)), A363120 phi(exp(-18*Pi)), A363021 phi(exp(-20*Pi)).

Sequence in context: A363081 A363020 A363178 * A363179 A292864 A363120

Adjacent sequences: A363116 A363117 A363118 * A363120 A363121 A363122

Keyword

nonn,cons

Author

Vaclav Kotesovec, May 15 2023

Status

approved