A292887 Decimal expansion of Product_{k>=1} (1 + exp(-3*Pi*k)).

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

Offset: 1

Author

Vaclav Kotesovec, Sep 26 2017

Keywords

• nonn
• cons

Examples

			1.000080706031033622547633753827481510343808241636336645922722085133112...
		

Links

• 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

Crossrefs

Cf. A292819, A292820, A292821, A292822, A292888.

Programs

Mathematica

RealDigits[(Sqrt[9 + 6*Sqrt[3]] - 2 - Sqrt[3])^(1/3) * E^(Pi/8)/ 2^(3/8), 10, 120][[1]]
RealDigits[QPochhammer[-1, E^(-3*Pi)]/2, 10, 120][[1]]

Formula

Equals (sqrt(9 + 6*sqrt(3)) - 2 - sqrt(3))^(1/3) * exp(Pi/8) / 2^(3/8).