A292888 Decimal expansion of Product_{k>=1} (1 - exp(-3*Pi*k)).

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

Offset

0,1

Links

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

Eric Weisstein's World of Mathematics, Dedekind Eta Function

Eric Weisstein's World of Mathematics, q-Pochhammer Symbol

Wikipedia, Dedekind eta function

Wikipedia, Euler function

Formula

Equals (5 - sqrt(3) + sqrt(2)*3^(3/4))^(1/6) * exp(Pi/8) * Gamma(1/4) / (2^(25/24) * 3^(3/8) * Pi^(3/4)).

Example

0.999919293970017559324282655320322884698349280317277031532319284136657...

Mathematica

RealDigits[(5 - Sqrt[3] + Sqrt[2]*3^(3/4))^(1/6) * E^(Pi/8) * Gamma[1/4] / (2^(25/24)*3^(3/8)*Pi^(3/4)), 10, 120][[1]]
RealDigits[QPochhammer[E^(-3*Pi)], 10, 120][[1]]

Prog

(PARI) (5 - sqrt(3) + sqrt(2)*3^(3/4))^(1/6) * exp(Pi/8) * gamma(1/4) / 2^(25/24) / 3^(3/8) / Pi^(3/4) \\ Charles R Greathouse IV, Sep 02 2024

Crossrefs

Cf. A292862, A292863, A259147, A259148, A259149, A259150, A259151, A292864.

Cf. A292887.

Sequence in context: A347220 A348294 A018938 * A111659 A346450 A102819

Adjacent sequences: A292885 A292886 A292887 * A292889 A292890 A292891

Keyword

nonn,cons

Author

Vaclav Kotesovec, Sep 26 2017

Status

approved