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A292862 Decimal expansion of Product_{k>=1} (1 - exp(-Pi*k/8)). 9

%I

%S 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,

%T 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,

%U 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

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

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/DedekindEtaFunction.html">Dedekind Eta Function</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/q-PochhammerSymbol.html">q-Pochhammer Symbol</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Dedekind_eta_function">Dedekind eta function</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Euler_function">Euler function</a>

%F 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)).

%e 0.061659166029172494376473069877211930625574501645956240930005560541903...

%t 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]]

%t RealDigits[QPochhammer[E^(-Pi/8)], 10, 120][[1]]

%o (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

%Y Cf. A259147, A259148, A259149, A259150, A259151, A292863, A292864.

%K nonn,cons

%O -1,1

%A _Vaclav Kotesovec_, Sep 25 2017

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Last modified February 27 15:58 EST 2020. Contains 332307 sequences. (Running on oeis4.)