A292864 Decimal expansion of Product_{k>=1} (1 - exp(-16*Pi*k)).

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

Offset

0,1

Links

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

Yu. V. Nesterenko, Modular functions and transcendence questions, Sbornik: Mathematics 187:9 (1996), pp. 1319-1348. (English translation)

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

Index entries for transcendental numbers.

Formula

Equals (3*sqrt(22*sqrt(2) - 24) - 8)^(1/8) * exp(2*Pi/3) * Gamma(1/4) / (2^(19/8) * Pi^(3/4)).

Example

0.999999999999999999999852096538403821434745775570049416313143433113717...

Mathematica

RealDigits[(3*Sqrt[-24 + 22*Sqrt[2]] - 8)^(1/8) * E^(2*Pi/3) * Gamma[1/4] / (2^(19/8)*Pi^(3/4)), 10, 120][[1]]
(* Alternative: *)
RealDigits[QPochhammer[E^(-16*Pi)], 10, 120][[1]]

Prog

(PARI) (3*sqrt(22*sqrt(2)-24)-8)^(1/8)*exp(2*Pi/3)*gamma(1/4)/(2^(19/8)*Pi^(3/4)) \\ Charles R Greathouse IV, Jul 06 2026

Crossrefs

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

Sequence in context: A363178 A363119 A363179 * A363120 A363021 A099646

Adjacent sequences: A292861 A292862 A292863 * A292865 A292866 A292867

Keyword

nonn,cons,changed

Author

Vaclav Kotesovec, Sep 25 2017

Status

approved