A057823 Decimal expansion of q = 0.193072033..., which is the value of q which gives the maximum of the Dedekind eta function eta(q) := q^(1/12) * Product_{n>=1} (1 - q^(2n)) for q between 0 and 1.

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

Offset: 0

Author

Peter L. Walker (peterw(AT)aus.ac.ae), Nov 24 2000

Keywords

• cons
• nonn
• easy
• nice

Examples

			0.19307203395741097892294168542126225457050776097870...
		

Links

• Eric Weisstein's World of Mathematics, Dedekind Eta Function.

Crossrefs

Cf. A211342.

Programs

Mathematica

RealDigits[FindRoot[D[q^(1/12)*Product[(1-q^(2 n)), {n, 100}], q] == 0, {q, 0.2}, WorkingPrecision -> 200][[1,2]]][[1]]
q /. Last @ FindMaximum[ DedekindEta[ -I*Log[q]/Pi], {q, 1/5}, WorkingPrecision -> 200] // RealDigits[#][[1]][[1 ;; 100]]&  (* Jean-François Alcover, Feb 05 2013 *)
q0 = q /. FindMaximum[q^(1/12)*QPochhammer[q^2], {q, 1/5}, WorkingPrecision -> 200][[2]]; RealDigits[q0, 10, 100][[1]] (* Jean-François Alcover, Nov 25 2015 *)

Formula

Equals sqrt(A211342). - Vaclav Kotesovec, Jul 02 2017

Extensions

More terms from Vladeta Jovovic, Jun 19 2004