A292863 Decimal expansion of Product_{k>=1} (1 - exp(-Pi*k/4)).

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

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 (6*sqrt(22*sqrt(2)-24) - 16)^(1/8) * exp(Pi/96)* Gamma(1/4) / (2*Pi^(3/4)).

Example

0.359892678203652899339430265542322684137982404699286565676073660815219...

Mathematica

RealDigits[(6*Sqrt[22*Sqrt[2] - 24] - 16)^(1/8) * E^(Pi/96) * Gamma[1/4] / (2*Pi^(3/4)), 10, 120][[1]]
RealDigits[QPochhammer[E^(-Pi/4)], 10, 120][[1]]

Crossrefs

Cf. A259147, A259148, A259149, A259150, A259151, A292862, A292864, A368211.

Sequence in context: A230725 A254689 A176445 * A160173 A256537 A092996

Adjacent sequences: A292860 A292861 A292862 * A292864 A292865 A292866

Keyword

nonn,cons

Author

Vaclav Kotesovec, Sep 25 2017

Status

approved