A292862 Decimal expansion of Product_{k>=1} (1 - exp(-Pi*k/8)).

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

Offset

-1,1

Links

Table of n, a(n) for n=-1..104.

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 (96*sqrt(2) - 136 + 3*sqrt(2792 - 1984*sqrt(2) + sqrt(849766*sqrt(2) - 1201560)))^(1/8) * (1 + sqrt(2))^(1/4) * exp(Pi/192) * Gamma(1/4) / (2^(13/16) * Pi^(3/4)).

Example

0.061659166029172494376473069877211930625574501645956240930005560541903...

Mathematica

RealDigits[(96*Sqrt[2] - 136 + 3*Sqrt[2792 - 1984*Sqrt[2] + Sqrt[849766*Sqrt[2] - 1201560]])^(1/8) * (1 + Sqrt[2])^(1/4) * E^(Pi/192) * Gamma[1/4] / (2^(13/16) * Pi^(3/4)), 10, 120][[1]]
RealDigits[QPochhammer[E^(-Pi/8)], 10, 120][[1]]

Prog

(PARI) sqrtn(96*sqrt(2) - 136 + 3*sqrt(2792 - 1984*sqrt(2) + sqrt(849766*sqrt(2) - 1201560)), 8)*sqrtn(1 + sqrt(2), 4)*exp(Pi/192)*gamma(1/4)/sqrtn(8192*Pi^12, 16) \\ Charles R Greathouse IV, Mar 13 2018

Crossrefs

Cf. A259147, A259148, A259149, A259150, A259151, A292863, A292864, A368211.

Sequence in context: A144544 A070514 A169886 * A070472 A320394 A151784

Adjacent sequences: A292859 A292860 A292861 * A292863 A292864 A292865

Keyword

nonn,cons

Author

Vaclav Kotesovec, Sep 25 2017

Status

approved